Worksheet: Volumes of Spheres

In this worksheet, we will practice finding volumes of spheres and solving problems including real-life situations.

Q1:

The radius of a sphere is 708 cm. Find its volume in terms of 𝜋.

  • A 4 2 3 6 𝜋 cm3
  • B 2 3 6 𝜋 cm3
  • C 9 4 4 𝜋 cm3
  • D 2 3 6 𝜋 cm3

Q2:

What is the volume of a sphere whose diameter is 30?

  • A 4 , 5 0 0 𝜋
  • B 3 6 , 0 0 0 𝜋
  • C 1 3 , 5 0 0 𝜋
  • D 3 0 0 𝜋
  • E36,000

Q3:

Find the diameter of a sphere whose volume is 113.04 cm3. (Take 𝜋=3.14).

Q4:

Which of the following formulae could be used to calculate the volume of the sphere?

  • A 𝑉 = 1 3 𝜋 𝑟
  • B 𝑉 = 4 3 𝜋 𝑟
  • C 𝑉 = 4 3 𝜋 𝑟
  • D 𝑉 = 𝜋 𝑟
  • E 𝑉 = 𝜋 𝑟

Q5:

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

Q6:

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

Q7:

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

Q8:

A sphere has a diameter of 18 cm. Work out the volume of the sphere, giving your answer in terms of 𝜋.

  • A 7 2 9 𝜋 cm3
  • B 9 7 2 𝜋 cm3
  • C 7 , 7 7 6 𝜋 cm3
  • D 2 7 𝜋 cm3
  • E 2 4 3 𝜋 cm3

Q9:

A football can be modeled as a sphere. If the football has a diameter of 20 cm, calculate its volume using this model, giving your answer accurate to two decimal places.

Q10:

Find the volume of a sphere whose diameter is 4.2 cm. Use 𝜋=227.

Q11:

Find the radius of a sphere whose volume is 92𝜋 cm3.

  • A 3 2 cm
  • B 3 2 2 cm
  • C 2 3 cm
  • D 2 3 cm

Q12:

The volume, 𝑉, of a sphere in terms of its radius, 𝑟, is given by 𝑉(𝑟)=43𝜋𝑟. Express 𝑟 as a function of 𝑉 and find, to the nearest tenth of a foot, the radius of a sphere whose volume is 200 cubic feet.

  • A 𝑟 = 3 𝑉 4 𝜋 , 3.6 feet
  • B 𝑟 = 3 𝑉 4 𝜋 , 6.9 feet
  • C 𝑟 = 4 𝑉 3 𝜋 , 4.4 feet
  • D 𝑟 = 4 𝑉 3 𝜋 , 20.2 feet
  • E 𝑟 = 3 𝑉 4 𝜋 , 16.7 feet

Q13:

Three-quarters of the volume of a sphere is 729𝜋 cm3. What is the radius of the sphere?

Q14:

Find, to the nearest tenth, the volume of a sphere given that the circumference of its great circle is 90𝜋 in.

Q15:

Find, to the nearest tenth, the volume of a sphere given that the area of its great circle is 400𝜋 in2.

Q16:

Benjamin opens a new 2 liters tub of ice cream and has three spherical scoops for dessert. Given that each scoop has a diameter of 40 mm, how many more whole scoops can he get from the tub?

Q17:

Two spheres have volumes of 162𝜋 and 3,072𝜋 cubic centimeters. What is the ratio of the radius of the small sphere to that of the large one?

  • A 8 3
  • B 2 7 5 1 2
  • C 5 1 2 2 7
  • D 3 5 1 2
  • E 3 8

Q18:

A sphere of metal with radius 14.1 cm was melted down and formed into 4 equal spheres. Find the radius of one of the smaller spheres, giving your answer to the nearest centimeter.

Q19:

A metal sphere of diameter 4 cm was melted down and reformed into a cylinder with a base radius of 6 cm. Find the height of the cylinder.

  • A 1 3 cm
  • B 8 2 7 cm
  • C 2 9 cm
  • D 2 3 cm

Q20:

A cuboid of lead has dimensions 154 cm by 48 cm by 42 cm. The cuboid is melted down to form a sphere. Using the approximation 𝜋=227, find the radius of the sphere formed.

Q21:

A hollow sphere of metal has an internal radius of 1.8 cm and an external radius of 2.2 cm. One cubic centimeter of the metal weighs 30 g. Using the approximation 𝜋=227, find the mass of the sphere.

Q22:

Find the radius of a sphere whose volume is 1,375,357.68 cm3. (Use 𝜋=3.14).

Q23:

The sphere and cylinder in the given figure are to be constructed with equal volumes.

Work out a formula for 𝑟 in terms of .

  • A 𝑟 = 1 3
  • B 𝑟 = 4 3
  • C 𝑟 = 3 2
  • D 𝑟 = 2 3
  • E 𝑟 = 3 4

Given that the height of the cylinder needs to be 18 inches, find the volume of the two solids. Give your answer to two decimal places.

Q24:

A hemisphere has a radius of 15 inches. Work out its volume, giving your answer in terms of 𝜋.

  • A 4 , 5 0 0 𝜋 cubic inches
  • B 1 5 0 𝜋 cubic inches
  • C 1 , 1 2 5 𝜋 cubic inches
  • D 3 0 0 𝜋 cubic inches
  • E 2 , 2 5 0 𝜋 cubic inches

Q25:

The base of a hemisphere has an area of 32𝜋 cm2. Work out the volume of the hemisphere giving your answer accurate to two decimal places.

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