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.

  • A4236𝜋 cm3
  • B236𝜋 cm3
  • C944𝜋 cm3
  • D236𝜋 cm3

Q2:

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

  • A4,500𝜋
  • B36,000𝜋
  • C13,500𝜋
  • D300𝜋
  • 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?

  • A𝑉=13𝜋𝑟
  • B𝑉=43𝜋𝑟
  • C𝑉=43𝜋𝑟
  • D𝑉=𝜋𝑟
  • E𝑉=𝜋𝑟

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.

  • A729𝜋 cm3
  • B972𝜋 cm3
  • C7,776𝜋 cm3
  • D27𝜋 cm3
  • E243𝜋 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.

  • A32 cm
  • B322 cm
  • C23 cm
  • D23 cm

Q12:

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

Q13:

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

Q14:

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

Q15:

Liam 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?

Q16:

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?

  • A83
  • B27512
  • C51227
  • D3512
  • E38

Q17:

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.

Q18:

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.

  • A13 cm
  • B827 cm
  • C29 cm
  • D23 cm

Q19:

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

Q20:

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.

Q21:

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

Q22:

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

Work out a formula for 𝑟 in terms of .

  • A𝑟=13
  • B𝑟=43
  • C𝑟=32
  • D𝑟=23
  • E𝑟=34

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.

Q23:

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

  • A4,500𝜋 cubic inches
  • B150𝜋 cubic inches
  • C1,125𝜋 cubic inches
  • D300𝜋 cubic inches
  • E2,250𝜋 cubic inches

Q24:

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

Q25:

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

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