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Worksheet: Volume of a Cone

In this worksheet, we will practice calculating the volume of a cone given its height and the area of its base.

Q1:

Determine the volume of the right circular cone in terms of πœ‹ .

  • A 1 6 0 πœ‹ cm3
  • B 9 6 0 0 πœ‹ cm3
  • C 3 2 0 πœ‹ cm3
  • D 3 2 0 0 πœ‹ cm3

Q2:

Determine the volume of the given right circular cone in terms of πœ‹ .

  • A 2 5 9 2 0 πœ‹ cm3
  • B 6 2 2 0 8 πœ‹ cm3
  • C 5 7 6 πœ‹ cm3
  • D 2 0 7 3 6 πœ‹ cm3

Q3:

Determine the volume of the given solid to the nearest hundredth.

Q4:

Work out the volume of a cone with a radius of 3 and a height of 14. Give your solution to two decimal places.

Q5:

The volume of a cone is 4 4 1 πœ‹ cubic inches, and its height is 12 inches. Find its diameter.

Q6:

A cone has a volume of 486 cubic centimeters. What is the volume of a cylinder that has the same radius and height as the cone?

Q7:

Victoria is making cone-shaped hats of diameter 4.2 inches and height 7.3 inches for a party. Find the volume of each cone in terms of πœ‹ .

  • A 3 2 . 1 9 3 πœ‹ in3
  • B 4 2 . 9 2 4 πœ‹ in3
  • C 5 . 1 1 πœ‹ in3
  • D 1 0 . 7 3 1 πœ‹ in3
  • E 7 4 . 6 0 6 πœ‹ in3

Q8:

Find, to the nearest tenth, the volume of an oblique cone with a diameter of 13 inches and an altitude of 15 inches.

Q9:

A traffic cone has a diameter of 15 cm and a height of 0.6 m. By modelling it as a solid cone, work out the volume of the traffic cone, giving your answer to the nearest cubic centimeter.

  • A 106 cm3
  • B 1 0 6 0 3 cm3
  • C 35 cm3
  • D 3 5 3 4 cm3
  • E 141 cm3

Q10:

Which is greater in volume, a right cone having a base radius of 25 cm and a height of 56 cm, or a right square pyramid having a base with a perimeter of 176 cm and a height of 48 cm?

  • Athe cone
  • Bthe pyramid

Q11:

Work out the volume of the cone, giving your answer accurate to two decimal places.

  • A 155.23 cm3
  • B 7 5 4 3 . 9 9 cm3
  • C 465.68 cm3
  • D 1 2 5 7 . 3 3 cm3
  • E 5 0 2 9 . 3 3 cm3

Q12:

Work out the volume of the cone, giving your answer accurate to two decimal places.

Q13:

Work out the volume of a cone with a diameter of 10.5 and a height of 11.3. Give your solution to two decimal places.

Q14:

If the radius of a cone was tripled but the volume stayed the same, what is relation between the new height β„Ž 𝑛 and the original height β„Ž π‘œ ?

  • A β„Ž = 3 β„Ž 𝑛 π‘œ
  • B β„Ž = 1 3 β„Ž 𝑛 π‘œ
  • C β„Ž = 9 β„Ž 𝑛 π‘œ
  • D β„Ž = 1 9 β„Ž 𝑛 π‘œ
  • E β„Ž = 1 6 β„Ž 𝑛 π‘œ

Q15:

Daniel wants to make three identical cones made from plaster for a school project. Each cone needs to be 5 inches tall and 2 inches in diameter. How many cubic inches of plaster will Daniel need to make his cones? Give your answer in terms of πœ‹ .

  • A 2 0 πœ‹ cubic inches
  • B 5 πœ‹ 3 cubic inches
  • C 3 πœ‹ 5 cubic inches
  • D 5 πœ‹ cubic inches
  • E 1 5 πœ‹ cubic inches

Q16:

A cone with a perpendicular height of 9 feet has a density of 6 lbs per cubic foot and a mass of 160 lb. Work out, to two decimal places, the radius of the cone, knowing that density = m a s s v o l u m e .

Q17:

Determine, to the nearest tenth, the volume of a right cone having a height of 106 cm, given that the perimeter of its base is 318 cm. Use πœ‹ = 2 2 7 .

Q18:

Completely immersing a metallic cone of height 45.63 cm in a cylinder of water raises the water level by 9 cm. What is the radius of the cylinder if the base radius of the cone is 41 cm? Give your answer to the nearest hundredth, if necessary.

Q19:

Determine, to the nearest hundredth, the volume of a cone of base diameter 32 and height 23.

Q20:

Which would have a greater effect on the volume of a cone, doubling its radius or doubling its height?

  • A doubling its radius
  • B doubling its height

Q21:

Find the volume of the cone. Give your answer in cubic millimeters to two decimal places.

Q22:

Given that the volume of a right circular cone is 643 cm3, determine its volume when its height and radius are doubled.

Q23:

Given that the volume of a right circular cone is 3 405 cm3, determine its volume when its height is doubled.

  • A 13 620 cm3
  • B 1 702.5 cm3
  • C 851.25 cm3
  • D 6 810 cm3
  • E 4 815.4 cm3

Q24:

Given that the volume of a right circular cone is 2 574 cm3, determine its volume when its radius is doubled.

Q25:

A cone has a perpendicular height of 92 inches and a volume of 4 2 0 πœ‹ cubic inches. Work out the radius of the cone, giving your answer to the nearest inch.

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