# What is the volume of the solid with given base and cross sections? The base is the region enclosed by y=x^2 and y=3. The cross sections perpendicular to the y-axis are rectangles of height y^3.

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1. ## Calc 2

Find the volume of the solid whose base is the region enclosed by y=x^2 and y=2, and the cross sections perpendicular to the y-axis are squares.

2. ## CALCULUS

The base of S is a circular disk with radius 3r. Parallel cross-sections perpendicular to the base are isosceles triangles with height 8h and unequal side in the base. a. set up an interval for volume of S b. by interpreting the intergal as an area, find

3. ## calculus

#3 A solid has a base in the form of the ellipse: x^2/25 + y^2/16 = 1. Find the volume if every cross section perpendicular to the x-axis is an isosceles triangle whose altitude is 6 inches. #4 Use the same base and cross sections as #3, but change the

4. ## Calculus 2

Find the volume of the solid whose base is the semicircle y= sqrt(1− x^2) where −1≤x≤1, and the cross sections perpendicular to the x -axis are squares.

5. ## Calculus

Find the volume of the solid whose base is the circle x^2+y^2=25 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal. Find the area of the vertical cross section A at the level x=1.

6. ## Calculus

The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid? 36 sqrt 3 36 18 sqrt 3 18 The answer isn't 18 sqrt 3 for sure.

7. ## Calculus

The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are squares. What is the volume, in cubic units, of the solid? A. 18 B. 36 C. 72 D. 144 Please help. Thank you in advance.

8. ## calculus

Find the volume V of the described solid S. The base of S is a circular disk with radius 2r. Parallel cross-sections perpendicular to the base are squares.

9. ## Calculus

Let R be the region enclosed by the graphs y=e^x, y=x^3, and the y axis. A.) find R B.) find the volume of the solid with base on region R and cross section perpendicular to the x axis. The cross sections are triangles with height equal to 3 times the

10. ## Calculus (Volume of Solids)

A solid has, as its base, the circular region in the xy-plane bounded by the graph of x^2 + y^2 = 4. Find the volume of the solid if every cross section by a plane perpendicular to the x-axis is a quarter circle with one of its radii in the base.

11. ## Calculus

Let R be the region in the first quadrant enclosed by the graph of f(x) = sqrt cosx, the graph of g(x) = e^x, and the vertical line pi/2, as shown in the figure above. (a) Write. but do not evaluate, an integral expression that gives the area of R. (b)

1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate, the integral which gives

13. ## Calculus

The base of a solid is the region enclosed by the graph of x^2 + 4y^2 = 4 and cross-sections perpendicular to the x-axis are squares. Find the volume of this solid. a. 8/3 b. 8 pi/3 c. 16/3 d. 32/3 e. 32 pi/3 Thanks in advance! :)

14. ## Calculus

The base of a solid in the xy-plane is the circle x^2+y^2 = 16. Cross sections of the solid perpendicular to the y-axis are semicircles. What is the volume, in cubic units, of the solid? a. 128π/3 b. 512π/3 c. 32π/3 d. 2π/3

15. ## Calculus

Find the volume of the solid whose base is the circle x^2+y^2=64 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal. Find the area of the vertical cross section A at the level x=7.

16. ## College Calculus

Find the volume of the solid with given base and cross sections. The base is the unit circle x^2+y^2=1 and the cross sections perpendicular to the x-axis are triangles whose height and base are equal.

17. ## Calculus

a solid has as its base the region bounded by the curves y = -2x^2 +2 and y = -x^2 +1. Find the volume of the solid if every cross section of a plane perpendicular to the x-axis is a trapezoid with lower base in the xy-plane, upper base equal to 1/2 the

18. ## Calculus I

The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are squares. What is the volume, in cubic units, of the solid?

19. ## Calculus

The base of a solid in the xy-plane is the first-quadrant region bounded y = x and y = x^2. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid? So I got 1/30 because (integral

20. ## Calculus

The base of a solid is bounded by the curve y=sqrt(x+1) , the x-axis and the line x = 1. The cross sections, taken perpendicular to the x-axis, are squares. Find the volume of the solid a. 1 b. 2 c. 2.333 d. none of the above I got a little confused, but

21. ## calculus

Find the volume of a solid whose base is bounded by the parabola x=y^2 and the line x=9, having square cross-sections when sliced perpendicular to the x-axis.

22. ## Calculus

The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y = 2. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units, of the solid?

23. ## Math

Find the volume V of the described solid S. The base of S is a circular disk with radius 4r. Parallel cross-sections perpendicular to the base are squares.

24. ## calculus

The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid?

25. ## calculus

Find the volume V of the described solid S. The base of S is an elliptical region with boundary curve 9x2 + 25y2 = 225. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

26. ## Calculus

The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid? 36√3 36 18√3 18

27. ## calculus

The base of a solid is bounded by the curve y= sort (x+2) ,the x-axis and the line x = 1. The cross sections, taken perpendicular to the x-axis, are squares. Find the volume of the solid.

28. ## Calculus

Let M be the region under the graph of f(x) = 3/e^x from x=0 to x=5. A. Find the area of M. B. Find the value of c so that the line x=c divides the region M into two pieces with equal area. C. M is the base of a solid whose cross sections are semicircles

29. ## Calculus

R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find

30. ## Calculus

The base of a solid is a circular disk with radius 3. Find the volume of the solid if parallel cross-sections is perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.

31. ## math

The base of a solid is a region bounded by the curve (x^2/64) + (y^2/16) = 1. Find the volume of the solid if every cross section by a plane perpendicular to the major axis (x-axis) has the shape of an isosceles triangle with height equal to 1/4 the length

32. ## math

Can someone please explain this problem to me: I have to use integrals to find volumes with known cross sections but i just don't understand. Thanks! Consider a solid bounded by y=2ln(x) and y=0.9((x-1)^3). If cross sections taken perpendicular to the

33. ## Calculus

Which of the following is not true? A. In a solid of revolution, the cross-sections are circles or washers. B. You can figure the volume of a solid by slicing it into cross- sections, figuring the individual volumes, and adding them up. C. You can figure

34. ## Calculus

Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. The region R is the base of a solid. For this solid, the cross sections, perpendicular to the

35. ## Calculus

The base of a solid is bounded by the curve y=√ x + 1, the x-axis and the line x = 1. The cross sections, taken perpendicular to the x-axis, are squares. Find the volume of the solid.

36. ## calculus

1. A solid is constructed so that it has a circular base of radius r centimeters and every plane section perpendicular to a certain diameter of the base is a square, with a side of the square being a chord of the circle. a. Find the volume of the solid. b.

37. ## Calculus

R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find

38. ## CALCULUS 2

Use calculus to find the volume of the following solid S: The base of S is an elliptical region with boundary curve 9x^2+4y^2=36. Cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

39. ## calculus

Find the volume of the solid S that satisfies the two following conditions. First, the base of S is the elliptical region with boundary curve 9 x2 + 4 y2 = 36, and second, the cross-sections of S perpendicular to the x-axis are isosceles right triangles

40. ## calculus

The base of a certain solid is the triangle with vertices at (−6,3), (3,3), and the origin. Cross-sections perpendicular to the y-axis are squares. Then the volume of the solid?

41. ## AP Calc

The base of a solid is the region in the first quadrant bounded by the ellipse x^2/a^2 + y^2/b^2 = 1. Each cross-section perpendicular to the x-axis is an isosceles right triangle with the hypotenuse as the base. Find the volume of the solid in terms of a

42. ## calculus

the base of a solid is a region in the first quadrant bounded by the x-axis, the y-axis, and the line y=1-x. if cross sections of the solid perpendicular to the x-axis are semicircles, what is the volume of the solid?

43. ## Calc

The base of a solid is a circle of radius a, and its vertical cross sections are equilateral triangles. The volume of the solid is 10 cubic meters. Find the radius of the circle.

44. ## Calculus II

Find the volume of the solid whose base is the semicircle y=sqrt(16−x^2) where −4 is less then or equal to x which is less then or equal to 4, and the cross sections perpendicular to the x-axis are squares.

45. ## calculus

Find the volume of the solid whose base is the region bounded between the curve y=sec x and the x-axis from x=pi/4 to x=pi/3 and whose cross sections taken perpendicular to the x-axis are squares.

46. ## Calculus

The base is an equilateral triangle each side of which has length 10. The cross sections perpendicular to a given altitude of the triangles are squares. How would you go about determining the volume of the solid described? The textbook answer is

47. ## Calculus BC

Let the region bounded by x^2 + y^2 = 9 be the base of a solid. Find the volume if cross sections taken perpendicular to the base are isosceles right triangles. (a) 30 (b) 32 (c) 34 (d) 36 (e) 38

48. ## Calculus

The base of a solid in the region bounded by the graphs of y = e^-x, y = 0, and x = 0, and x = 1. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid? Answers: 1)(pi/16)e^2

49. ## Calculus

The base of a solid is bounded by y=2sqrtx, y=2 and x=4. Find the volume of solid if cross sections perpendicular to y=2 are semicircles

50. ## Calculus

The base of a certain solid is the triangle with vertices at (-14,7),(7,7) and the origin. Cross-sections perpendicular to the y-axis are squares. What is the volume of this solid?

51. ## Calculus

The base of a solid in the xy-plane is the circle x^2 + y^2 = 16. Cross sections of the solid perpendicular to the y-axis are equilateral triangles. What is the volume, in cubic units, of the solid? answer 1: (4√3)/3 answer 2: (64√3)/3 answer 3:

52. ## calculus

The base of a solid is a circle of radius = 4 Find the exact volume of this solid if the cross sections perpendicular to a given axis are equilateral right triangles. The equation of the circle is: x^2 + y^2 = 16 I have the area of the triangle (1/2bh) to

53. ## calc

The base of a three-dimensional figure is bound by the line y = 6 - 2x on the interval [-1, 2]. Vertical cross sections that are perpendicular to the x-axis are rectangles with height equal to 2. Find the volume of the figure. The base of a

54. ## mathematics

The base of a certain solid is the triangle with vertices at (−12,6), (6,6), and the origin. Cross-sections perpendicular to the y-axis are squares.

55. ## Calculus

Find the volume of the solid whose base is the region in the xy-plane bounded by the given curves and whose cross-sections perpendicular to the x-axis are (a) squares, (b) semicircles, and (c) equilater triangles. y=x^2, x=0, x=2, y=0 I know how to graph

56. ## Calculus AP

Let R be the region in the first quadrant bounded by the graph y=3-√x the horizontal line y=1, and the y-axis as shown in the figure to the right. Please show all work. 1. Find the area of R 2. Write but do not evaluate, an integral expression that gives

57. ## Calculus

This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of the solid formed by

58. ## calc

What is the volume of the solid with given base and cross sections? The base is the region enclosed by y=x^2 and y=3. The cross sections perpendicular to the y-axis are rectangles of height y^3.

59. ## Calculus

Hi, I have a calculus question that I just cannot figure out, it is about volume of cross sections. I would very much appreciate it if someone could figure out the answer and show me all the steps. A solid has as its base the region bounded by the curves y

60. ## Calculus

Hi, I have a calculus question that I just cannot figure out, it is about volume of cross sections. I would very much appreciate it if someone could figure out the answer and show me all the steps. A solid has as its base the region bounded by the curves y

61. ## Calculus

The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x+y =4. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units , of the solid? A) 8 B)

62. ## math

Let M be the region under the graph f(x) = 3/(e^x) from x = 0 to x = 5. M is the base of a solid whose cross sections are semicircles whose diameter lies in the xy plane. The cross sections are perpendicular to the x-axis. Find the volume of this solid. -

63. ## math

Can someone please explain this problem to me: I have to use integrals to find volumes with known cross sections but i just don't understand. Thanks! Consider a solid bounded by y=2ln(x) and y=0.9((x-1)^3). If cross sections taken perpendicular to the

64. ## Calculus

Find the volume of the solid whose base is the region bounded by y=x^2 and the line y=0 and whose cross sections perpendicular to the base and parallel to the x-axis are semicircles.

65. ## AP Calc B/C

The base of a solid is the region enclosed by y=x^3 and the x-axis on the interval [0,4]. Cross sections perpendicular to the x-axis are semicircles with diameter in the plain of the base. Write an integral that represents the volume of the solid. I drew a

66. ## Calculus

The base of a solid is the circle x^2+y^2=9. Cross sections of the solid perpendicular to the x-axis are semi-circles. What is the volume, in cubics units, of the solid? a) 9 π/4 b) 18π c) 9π d) 72π

67. ## calculus

The base of a certain solid is the triangle with vertices at (-10,5), (5,5), and the origin. Cross-sections perpendicular to the y-axis are squares. What is the volume of the solid?

68. ## calculus

volume of solid whose base is a circle with radius a, and cross sections of the solid cut perpendicular to the x-axis are squares

69. ## calculus

the region bounded by the quarter circle (x^2) + (y^2) =1. Find the volume of the following solid. The solid whose base is the region and whose cross-sections perpendicular to the x-axis are squares.

70. ## Calculus (Volumes)

A solid has as its base the region bounded by the curves y = -2x^2 +2 and y = -x^2 +1. Find the volume of the solid if every cross section of a plane perpendicular to the x-axis is a trapezoid with lower base in the xy-plane, upper base equal to 1/2 the

71. ## Calculus

compute the volume of the following solid the base is a triangular region with vertices (0,0), (2,0), (1,1). Cross-sections perpendicular to the y-axis are equilateral triangles.

72. ## Calculus

A solid has as its base a circular region in the xy plane bounded by the graph of x^2 + y^2 = 4. Find the volume of a solid if every cross section by a plane perpendicular to the x-axis is an isosceles triangle with base on the xy plane and altitude equal

find the volume of the solid whose bounded by the circle x^2+y^2=4 and whose cross sections perpendicular to the y-axis are isosceles right triangles with one leg in the base. Please give explanation and steps

74. ## calc

the base of s is a elliptical region with boudary cuvrve 16x^2 +16y^2 =4. cross sections perpandicular to the x axis are isosceles right triangles with hypotenuse in the base. find the volume of s

75. ## Calc

The base of a solid is the unit circle x^2 + y^2 = 4, and its cross-sections perpendicular to the x-axis are rectangles of height 10. Find its volume. Here's my work: A for rectangle=lw A=10*sq(4-x) V= the integral from -4 to 4 of sq(4-x^2)*10dx But that

76. ## Calculus check

Can someone check my answers: 1) Use geometry to evaluate 6 int 2 (x) dx where f(x) = { |x|, -2

77. ## calculus

Find the volume V of the described solid S. The base of S is the region enclosed by the parabola y = 3 − 2x2 and the x−axis. Cross-sections perpendicular to the y−axis are squares.

78. ## calculus

The base of a solid consists of the region bounded by the parabola y=rootx, the line x=1 and the x-axis. Each cross section perpendicular to the base and the x-axis is a square. Find the volume of the solid.

79. ## Calculus

I would like to make sure my answer is correct: Question: the base of a solid is the triangular region with the vertices (0,0), (2,0), and (0,4). Cross sections perpendicular to the x-axis are semicircles. Find the volume of this solid. My Work: ∫[0,2]

80. ## Calculus

R is the region in the plane bounded below by the curve y=x^2 and above by the line y=1. (a) Set up and evaluate an integral that gives the area of R. (b) A solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find

81. ## math

Can someone please explain this problem to me: I have to use integrals to find volumes with known cross sections but i just don't understand. I have to do a lot of examples for homework like this so can someone show me so I can do my other problems?

82. ## calc

he base of a solid in the xy-plane is the circle x^2 + y^2 = 16. Cross sections of the solid perpendicular to the y-axis are semicircles. What is the volume, in cubic units, of the solid?

83. ## Calculus

The base of a solid is the circle x2 + y2 = 9. Cross sections of the solid perpendicular to the x-axis are semi-circles. What is the volume, in cubic units, of the solid?

84. ## calc

The base of a solid in the region bounded by the graphs of y = e^-x y = 0, and x = 0, and x = 1. Cross sections of the solid perpendicular to the x-axis are semicircles. What is the volume, in cubic units, of the solid?

85. ## calculus

The base of a solid in the xy-plane is the first-quadrant region bounded y = x and y = x2. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid?

86. ## Calculus

The base of a solid is the region bounded by the lines y = 5x, y = 10, and x = 0. Answer the following. a) Find the volume if the solid has cross sections perpendicular to the y-axis that are semicircles. b) Find the volume if the solid has cross sections

87. ## calculus

The base of a certain solid is the triangle with vertices at (-10,5), (5,5), and the origin. Cross-sections perpendicular to the y-axis are squares. What is the volume of the solid?

88. ## Calculus

The base of a solid in the xy-plane is the first-quadrant region bounded y = x and y = x^2. Cross sections of the solid perpendicular to the x-axis are equilateral triangles. What is the volume, in cubic units, of the solid? May I have all the explanation

89. ## Calculus

The base of a solid is a region located in quadrant 1 that is bounded by the axes, the graph of y = x^2 - 1, and the line x = 2. If cross-sections perpendicular to the x-axis are squares, what would be the volume of this solid?

90. ## calculus

The base of a solid V is the region bounded by y=(x^2/64) and y=sq(x/8) Find the volume if V has square cross sections

91. ## calculus

The base of a certain solid is the triangle with vertices at (-14,7), (7,7), and the origin. Cross-sections perpendicular to the y-axis are squares. What is the volume?

92. ## Calculus (area of base and volume of solid)

Can you check my work and see if I did the problem correctly? Thanks! A solid with a base formed by intersecting sine and cosine curves and built up with semi-circular cross-sections perpendicular to the x-axis. Find the area of the base and the volume of

93. ## calculus

find the volume of the solid whose base is bounded by the graphs of y= x+1 and y= (x^2)+1, with the indicated cross sections taken perpendicular to the x-axis. a) squares b) rectangles of height 1 the answers are supposed to be a. 81/10 b. 9/2 help with at

94. ## math

ind the volume of the solid whose base is bounded by the graphs of y= x+1 and y= (x^2)+1, with the indicated cross sections taken perpendicular to the x-axis. a) squares b) rectangles of height 1 the answers are supposed to be a. 81/10 b. 9/2 help with at

95. ## math

find the volume of the solid whose base is bounded by y=e^(-x), y=3cos(x), and x=0 and whose cross sections cut by planes perpendicular to the x-axis are squares the answer is 3.992 units cubed but can someone explain to me how to get this answer using

96. ## Calculus

The base of a certain solid is the triangle with vertices at (-10,5), (5,5), and the origin. Cross-sections perpendicular to the y-axis are squares.

97. ## calculus

The base of a certain solid is the triangle with vertices at (-10,5), (5,5), and the origin. Cross-sections perpendicular to the y-axis are squares.

98. ## calculus

Find the volume of the solid whose base of a solid is the region bounded bythegraphsofy=3x,y=6,andx=0. Thecross␣sections perpendicular to the x ␣ axis are rectangles of perimeter 20.

99. ## calculus

Find the volume of the solid whose base of a solid is the region bounded bythegraphsofy=3x,y=6,andx=0. Thecross␣sections perpendicular to the x ␣ axis are rectangles of perimeter 20.

100. ## calculus

The base of a solid is a circle of radius = 4 Find the exact volume of this solid if the cross sections perpendicular to a given axis are equilateral right triangles. I have the area of the triangle (1/2bh) to be equal to 2sqrt(12) (1/2 * 4 * sqrt12) I