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 given solid to the nearest hundredth.

Q2:

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

Q3:

Determine the volume of the right circular cone in terms of 𝜋 .

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

Q4:

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

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

Q5:

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.

Q6:

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

Q7:

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 = 2 2 7 .

Q8:

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?

Q9:

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

Q10:

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

Q11:

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

Q12:

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

Q13:

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

Q14:

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

Q15:

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

Q16:

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

Q17:

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

Q18:

If the radius of a cone was tripled but the volume stayed the same, what is relation between the new height 𝑛 and the original height 𝑜 ?

  • A = 3 𝑛 𝑜
  • B = 1 3 𝑛 𝑜
  • C = 9 𝑛 𝑜
  • D = 1 9 𝑛 𝑜
  • E = 1 6 𝑛 𝑜

Q19:

A cone with a perpendicular height of 9 feet has a density of 6 lb 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 .

Q20:

Yara 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 .

  • A in3
  • B in3
  • C in3
  • D in3
  • E in3

Q21:

Fares 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 Fares need to make his cones? Give your answer in terms of .

  • A cubic inches
  • B cubic inches
  • C cubic inches
  • D cubic inches
  • E cubic inches

Q22:

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.

Q23:

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

Q24:

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

Q25:

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

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