# 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?

1. 👍
2. 👎
3. 👁
1. How are the cross-sections oriented?

perp. to an axis, parallel to x+y=2, or some other way?

1. 👍
2. 👎
2. that is all the information given

1. 👍
2. 👎
3. well, it ain't enough. If the cross-sections are perpendicular to the x- (or y-)axis, then each thin plate has base of width 2-x, so

v = ∫[0,2] (2-x)^2 dx = 8/3

If the cross-sections are parallel to the line x+y=2, then each thin slice has base √(x^2+y^2) = √(x^2+(2-x)^2), so

v = ∫[0,2] x^2+(2-x)^2 dx = 16/3

1. 👍
2. 👎
4. Steve you’re so annoying bro don’t answer the questions if ur gonna keep on !@#\$%^&ing

1. 👍
2. 👎
5. Actually Steve is correct, it's the question that's wrong here. Normally, the answer should have been 8/3 assuming you had only found the area on just one half of the figure but Steve multiplied this by 2 to get the entire figure (since there are squares on both sides given that the left and right directions are perpendicular to the base). Hope this makes sense

1. 👍
2. 👎
6. Mathematics.

1. 👍
2. 👎
7. so whats the answer

1. 👍
2. 👎

## Similar Questions

1. ### 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

2. ### Math- Ms. Sue? Steve? Writeacher?

Point A(4,2) is translated according to the rule (x,y)-->(x+1,y-5) and then reflected across the y axis a)In which quadrant of the coordinate plane is point A located? b) What are the coordinates of translated point A'? in which

3. ### 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.

4. ### math

In which quadrant does the terminal side of the angle with measure -245 degree lie? Quadrant I Quadrant IV Quadrant III Quadrant II None

1. ### 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

2. ### algebra

1.What is the slope of the function shown on the graph? A line is graphed on a four quadrant coordinate plane. The x-axis and the y-axis go from negative 10 to 10 in increments of 1. The line passes through (0, 7) and (4, 2).

3. ### calculus review please help!

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,

4. ### calculus

The base of a solid is the region in the first quadrant bounded by the graph of y = 3/(e^x) , the x-axis, the y-axis, and the line x=2. Each cross section of this solid perpendicular to the x-axis is a square. What is the volume

1. ### 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

2. ### 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

3. ### Linear Functions

If m < 0 and b > 0, the graph of y = mx + b does not pass through which quadrant? Quadrant I Quadrant II Quadrant III Quadrant IV

4. ### 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