# A paper cup has the shape of a cone with height of 8cm and a radius of 4cm at the top. Water is poured into the cup at a rate of 2cm^3/s. How fast is the water level rising when

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1. ## Calculus

Given a right circular cone, you put an upside-down cone inside it so that its vertex is at the center of the base of the larger cone, and its base is parallel to the base of the larger cone. If you choose the upside-down cone to have the largest possible

2. ## calculas

4.A paper cup, which is in the shape of a right circular cone, is 16 cm deep and has a radius of 4 cm. Water is poured into the cup at a constant rate of . 3 2cm / sec (a) At the instant the depth is 5 cm, what is the rate of change of the height? (b) At

3. ## Calculus

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 16 feet

4. ## math

Two right circular cone, one upside down in the other. The two bases are parallel. The vertex of the smaller cone lies at the center of the larger cone’s base. The larger cone’s height and base radius are 12 and 16 ft, respectively. What are the

5. ## Math

Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 25

6. ## Calculus Help Please Urgent!!!

A cone-shaped paper drinking cup is to be made to hold 30 cm^3 of water. Find the height and radius of the cup that will use the smallest amount of paper. (Round your answers to two decimal places.) Height = ? Radius = ? Show work please!!!

7. ## Mathematics

a paper cone has a base diameter of 8cm and a height of 3cm.calculate the volume of the cone in terms of pie and make a sketch of the cone and hence use Pythagoras theorem to calculate its slant height and calculate the curve surface area of the cone in

8. ## math

A paper cup has the shape of a cone with height of 8cm and a radius of 4cm at the top. Water is poured into the cup at a rate of 2cm^3/s. How fast is the water level rising when the water level is 4cm deep?

9. ## calculus

water is poured into a conical paper cup so that the height increases at the constant rate of 1 inch per second. if the cup is 6 inches tall and its top has a radius of 2 inches, how fast is the volume of water in the cup increasing when the height is 3

10. ## math

Dana takes a sheet of paper, cuts a 120-degree circular sector from it, then rolls it up and tapes the straight edges together to form a cone. Given that the sector radius is 12 cm, find the height and volume of this paper cone.

A paper cup has the shape of a cone with height 8cm and radius 3cm at the top. Water is being poured into the cup at the rate of 2cm3/s. How fast is the water level rising when the water is 6cm deep?

12. ## Mathematics

A sector of a circle radius 8cm subtends and and angle 90°a at the centre of a circle. If the sector is folded without overlap to form the curved surface of a cone, find the 1. Base radius 2. Height 3. Volume of the cone.

13. ## Calculus (Math 2A)

Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 19

14. ## geometry

11. Infinitely many different sectors can be cut from a circular piece of paper with a 12-cm radius, and any such sector can be fashioned into a paper cone with a 12-cm slant height. (a) Show that the volume of the cone produced by the 180-degree sector is

15. ## math

A paper cone has a base diameter of 8cm and a height of 3cm a. Calculate the volume of the cone in term of pie b. Calculate the curve surface area of the cone

16. ## Calc

A paper cup is to be designed in the shape of a right circular cone. It must have a capacity of 12 fluid ounces (1 fluid ounce = 1.80469 cubic inches) of soft drink but it must use a minimum amount of material in its construction. What should the

17. ## geometry

A cone is created from a paper circle with a 90° sector cut from it. The paper along the remaining circumference of the circle is the base of the cone. Find the radius of the base of the cone. Round to the nearest hundredth.

18. ## maths

a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of cone is

19. ## PreCalculus

Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), cut out a sector with an arc of length x. Join the two radial edges of the remaining portion of the paper to form a cone with radius r and height h, as shown in

20. ## Maths

If a marble of radius 2.1 cm is put into a cylindrical cup of radius 6cm and height 8cm, then how much water flows out of it.?

21. ## Geometry

Infinitely many different sectors can be cut from a circular piece of paper with a 12-cm radius, and any such sector can be fashioned into a paper cone with a 12-cm slant height. (a) Show that the volume of the cone produced by the 180-degree sector is

22. ## Math

Janna is using a cone-shaped cup to fill a cylindrical container. The cup has the same height and radius as the container. How many times will she have to fill the cylindrical container? A. 1/3 B. 1 C. 2 D. 3 It didn't show the numbers for the radius or

23. ## calculus

water in a paper conical filter drips into a cup. let x denote the height of the water in the cup. if 10 in^3 of water are poured into the filter, find the relationship between dy/dt and dx/dt so the paper filter is 4 inches tall whith a radius of 2

24. ## calculus inverted cone

A container in the shape of an inverted cone has radius 6 ft and height 12 ft. It is being drained at 2〖ft〗^3/min. Find the rate of change of the height of the liquid in the cone when the height is 3 feet. The ratio of the radius to the height remains

25. ## calculus

Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 24

26. ## MATH214

Find the surface area of a right circular cone topped with a hemisphere. the height of the cone is 8cm, the radius is 4cm.

27. ## Math

2 part question 1) a cone shaped paper cup has a height of 7 inches and a diameter of 5 inches. What is the volume of the cone? Round answer to the nearest hundredth. 2) if we collect rainwater in the cup in question 1 until the waters depth is 6 inches,

28. ## Maths

(1) A cone has height of 8cm and circular radius 6cm calculate (a) It's Volume (b) It's Slant Height (c) The Curved Surface Area (d) The Total Surface Area

29. ## Math

A paper cone has a base diameter of 8cm and a height of 3cm(a) use Pythagoras theorem to calculate it's slant height (b)if the cone is cut and opened out into the sector of a circle what is the angel of the sector

30. ## Algebra/Geometry

I am eating a snow cone in a paper cone with a height of 21cm and the radius of my snow cone ice is 3.25 cm. Find the amount of material needed to make my paper snow cone

31. ## math

Mrs P made punch and wanted to serve it in cone shaped cups. When she poured the drink into the cup she poured it to the top and still had some remaining in the bowl. Mrs P knew that she made 355ml of punch. The height of the cone shaped cup was 12cm and

32. ## Math ( Palette of Problem)s)

A cone shaped paper cup has a height of 7 inches and a diameter of 5 inches. What is the volume of the cone round your answer to the nearest hundredth.

33. ## Geometry

A cone has a slant height of 15cm. The true height is 12 and the radius "r" is unknown. True height 12 and the radius intersect at a perpendicular angle inside the cone. What is the surface area of the entire cone?

34. ## math

calculate the total surface area of a solid cone of slant height 15cm and base radius 8cm in terms of π

35. ## Math

1. What is the length of the radius of the larger cone? The slant height of cone A is 12 and the radius is 8 The slant height of cone B is 15, I am trying to figure out the radius of this one... How do I do it? A:10 B:11 C:12 D:13 2. What is the length of

36. ## geometry and measurement

A Cone-shaped piece of paper has a height of 15 centimeters and a radius of 1.2 centimeters. The cone is 2/3 filled with sand. What is the approximate volume of the portion of the cone not filled with sand?

37. ## calculus ( related rates )

a paper cup in the shape of a cone has a diameter of 10cm across the top, and is 8cm deep. if the cup is leaking out the bottom at 2pi cm^3/min, at what rate is thet area of the water surface ( only the top surface of the water) changing, when the cup has

38. ## Calculus

A vessel is in the shape of an inverted cone. The radius of the top is 5cm and the height is 8cm. Water is poured into a height of xcm. Show that if the volume of the water is Vcm^3,then V=(25/192)*pi*x^3. (The volume of a cone is given by the formula

39. ## math

a piece of paper in the shape of sector of circle is rolled up to form a right circular cone. what is the measure of the angle theta if its height is twelve centimeter and radius is 5 cms

40. ## mathematics

The surface area of the ice cream cone shown below is given by A = 𝜋r2 +𝜋rs, where r is the radius of the circular top of the ice cream cone and s is the slant height of the cone. If the area of the cone is 12.16π in2 and the slant height of the

41. ## Pre-Algebra

The cones below are similar, although not drawn to scale. What is the length of the radius of the larger cone? The height of the smaller cone is 18 and the radius is 6. The height of the larger cone is 27 and the radius is unknown. A- 4 B- 6 C- 9 D- 12

42. ## Calc

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 14 feet

43. ## Mathematics

A sector of a circle of radius 8cm is bent to form a cone.find the radius of the cone and its vertical angle if the angle subtended at the centre by the sector is 280

44. ## Math

Sue bought an ice cream cone from Dairy Queen. The cone had a radius of 3cm and a height of 8cm. If I use the formula of (TT=3.14, r=radius, h=height) 2 V=1/3TTr h Is the answer 50.24 cm3? Any help is appreciated. If I'm not right could you tell/show me

45. ## Math

A conical paper cup is to have a height of 3 inches. Find the radius r of the cone that will result in a surface area of 6ðin^2.

46. ## CALCULUS

A cone shaped paper drinking cup is to be made from a circular piece of paper of radius 3 inches by cutting out a sector of the circle and gluing the straight edges together. Find the angle of the cut that gives the cup with the largest capacity.

47. ## geometry

The circumference of the top rim of the cone-shaped paper cup is 7.17 inches. Find the least amount of paper that can form the cone-shaped cup. (Round your answer to two decimal places.

48. ## calculus

A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way

49. ## Calculus

A cone is inscribed in a sphere of radius a, centred at the origin. The height of the cone is x and the radius of the base of the cone is r, as shown in the diagram opposite. Find the height, x, for which the volume of the cone is a maximum. (HINT: show

50. ## Math

A tank in the shape of a cone has a diameter of 8 feet and a height of 10 feet.when there is water in the tank, th water is in the shape of a cone too. find the radius of the cone of water when the water is 2 feet high. Explain how you would solve it.

51. ## Cranborne

In the diagram AOBP is the major sector of a circle centre O.BO=8cm, AOB=156° and the sector is bent to form a right cone. a)Caculate the radius of the cone b)Calculate the vertical angle of the cone

52. ## math

A cone of fixed height 12 inches is changing in shape through the change in the radius of the base. What rate of increase of the radius will make the lateral surface area of the cone increase at the rate of 10 ! square inches per minute when the radius of

53. ## Related Rates

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 25

Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 24

55. ## Calculus

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 18 feet

56. ## math

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 14 feet

Dimensions of a paper cup. The volume of a paper cup, shaped like a circular cone is 30pie cubic centimeters. The radius of the top of the cup is 3 centimeters. What is the height of the cup?

58. ## math

the paper hats are in the shape of a cone. the radius of the cone in 8 cm and the slant height is 20 cm. how many square centimeters of paper are needed to make each hat?

59. ## math

A paperweight containing liquid is made up of a cone and a cylinder. The radius of the cone is 3cm with height of 4cm. The diameter is 20cm and height is 8cm. 1. Calculate the total volume of the cone and cylinder when it si empty, leaving your answer in

60. ## Geometry

A snowcone with a radius of 4 cm is sold in a cone-shaped paper cup with a height of 12 cm and an opening 6 cm wide. If all the ice melted in the cup, would it overflow?

61. ## math

Midson draws a cone shape paper with height of 9 centimeters and a volume of 48 pi centimeters. What is the diameter of Midsons paper cup plz show all work

62. ## mathematics

a paper cone cone has a base diameter of 8cm and a height of 3cm solve

63. ## Mathematics

A paper cone has a base diameter of 8cm and a height of 3cm calculate the volume of the cone in terms of pi

64. ## Calculus

Suppose that sand is collecting in the shape of a cone in such a way that the base radius of the cone is always one-third of its height. If 3cm^3/min is the rate at which the sand is being added to the cone, how fast is the height of the cone changing when

65. ## maths

a paper cone has a base diameter of 8cm a height of 3cm. a)caculate the volume of the cone in terms of pie b)if the cone is cut and opened out into the sector of a circle.what is the angle of the sector

66. ## Math

A cylinder is inscribed in a cone as shown in the diagram below. The cone has a height of 8cm and a fixed radius of R cm. The cylinder has a radius of x cm and a height of h cm. Show that the volume of the cylinder is maximised when x=kR, where k is a

67. ## Mathematics

A paper cone has a base diameter of 8cm and a height of 3cm. Calculate the curved surface area of the cone in terms of p¹ (pie)

68. ## math

A right cone has a height of 8cm and of volume of 250cm^3. Determine the radius of the base of the cone to the nearest centimeter.

69. ## MATH214

Find the surface area of a right circular cone topped with a hemisphere. the height of the cone is 8cm, the radius is 4cm.

70. ## Math

Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), cut out a sector with an arc of length x. Join the two radial edges of the remaining portion of the paper to form a cone with radius r and height h, as shown in

71. ## Maths

A hemispherical paper is folder into a hallow right circular cone. The radius of the hemispherical paper is 12cm. What's the cone's base radius, height and volume?

72. ## maths

Im confused can any1 help me on this question ?? or try and put me on the right track? (a) A circle has radius 2cm (in that circle there is an triangle AOB) and the chord AB has length 3cm. AO is 2cm and BO is 2cm. O is the centre of the circle. (b)

73. ## calc (plz, with steps and explanations)

A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way

74. ## calculus

A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way.

75. ## math (explanation and answer)

A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way

76. ## calc (with through steps)

A conical drinking cup is made from a circular piece of paper of radius R inches by cutting out a sector and joining the edges CA and CB. Find the radius, height and volume of the cone of greatest volume that can be made this way

77. ## MATHEMATICS

A SECTOR IS USED TO FORM ACONE IF THE RADIUS AND ANGLE OF THESECTOR IS 8CM AND 160 DEGREE RESPECTIVELY CALCULATE, THE RADIUS OF THE CONE ,VERTICAL HEIGHT, VERTICAL ANGLE, VOLUME AND TOTAL SURFACE AREA OF THE CONE

78. ## Math

A conical paper cup for holding popcorn has a radius of 3 in. and height of 6 in. How much paper, to the nearest square inch, is used to make the cup?

79. ## Math

A conical paper cup for holding popcorn has a radius of 3 in. and height of 6 in. How much paper, to the nearest square inch, is used to make the cup?

80. ## Math

I already posted this, but wanted to say that I have the answers and it is 1.68 is less than or equal to x is less than or equal to 9.10 Cone Problem Beginning with a circular piece of paper with a 4- inch radius, as shown in (a), cut out a sector with an

81. ## geom. word problem

A soft-drink cup is in the shape of a right circular cone with capacity 250 milliliters. The radius of the circular base is 6 centimeters. How deep is the cup?

82. ## Calculus HARD NEED HELP

The volume of a cone of radius r and height h is given by V=(1/3)pir^2h. If the radius and the height both increase at a constant rate of 2cm/s at which rate in cubic cm/s is the volume increasing when the height is 8cm and the radius is 6cm. So The answer

83. ## Calculus

The volume of a cone of radius r and height h is given by V=(1/3)pir^2h. If the radius and the height both increase at a constant rate of 2cm/s at which rate in cubic cm/s is the volume increasing when the height is 8cm and the radius is 6cm. So The answer

84. ## math

I want to know how to calculate the radius, Im very confused. The cones below are similar, although not drawn to scale (smaller cone) (larger cone) height is 12 ft height is 15 ft radius is 8 ft radius not given What is the lenght of the radius of the

85. ## Calculus: Optimization

I have no idea how to approach this problem, if someone knows just how to relate h, r with H,R, that would be extremely helpful and I can workout the rest! Thank you in advance. Given a right circular cone, you put an upside-down cone inside it so that its

86. ## Math

A cone shaped paper cup has a height of 7 inches and a diameter of 5 inches. What is the volume of the cone? Round to the nearest hundreth

87. ## Mathematics

A paper has a base diameter of 8cm and height 3cm (a) use pythagoras theorem to calculate its slant height (b) if the cone is cut and opened out into the sector of a circle what is the angle of the sector

88. ## maths

if a hollow sphere of internal and external diameter 4cm melted 8cm respectively melted into a cone of base diameter 8cm . find the height of cone

89. ## Mathematics

solid is in the form of a cone mounted on himispher in such away that the Venter of the base of the cone fast coincide with the center of the base of the hemisphere.the radius of hemisphere and height of cone are r each ,radius of base of cone is 1/2r and

90. ## MATHEMATICS

Find the curved and total surface area of a right circular cone,of base radius 8cm and height 10cm

91. ## Math

A small cone has a vertex touching the base of a large cone. The base of the small cone is parallel to the base of the larger cone. a.) Find h and r so that the smaller cone has a maximum volume. b.) State the maximum volume c.) explain how you know

92. ## MATH

A cone-shaped cup is made from a circular piece of paper of radius 12 by cutting out a sector and joining the edges AC and BC.

93. ## African church grammar sch

Cal d total surface area of a solid cone of slant height 15cm and base radius 8cm in term of pie

94. ## calculus

Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the pile increasing when the

95. ## Math

Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 11 feet

96. ## calculus

Gravel is being dumped from a conveyor belt at a rate of cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the pile increasing when the pile

97. ## Calculus

Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the pile increasing when the

98. ## math

A cone with height 8 and radius 2 is sliced halfway along its height by a plane that is parallel to the base of the cone. What is the radius of the circle at the intersection of the plane and the cone?

99. ## Math

Gravel is being dumped from a conveyor belt at a rate of 50 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 17 feet

100. ## MATH

Gravel is being dumped from a conveyor belt at a rate of 10 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 14 feet