# 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 cm. Find its volume in terms of .

• A cm3
• B cm3
• C cm3
• D cm3

Q2:

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

• A
• B
• C
• D
• E36,000

Q3:

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

Q4:

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

• A
• B
• C
• D
• E

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 .

• A cm3
• B cm3
• C cm3
• D cm3
• E 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 .

Q11:

Find the radius of a sphere whose volume is cm3.

• A cm
• B cm
• C cm
• D cm

Q12:

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

• A , 3.6 feet
• B , 6.9 feet
• C , 4.4 feet
• D , 20.2 feet
• E , 16.7 feet

Q13:

Three-quarters of the volume of a sphere is 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 in.

Q15:

Find, to the nearest tenth, the volume of a sphere given that the area of its great circle is 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 and cubic centimeters. What is the ratio of the radius of the small sphere to that of the large one?

• A
• B
• C
• D
• E

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 cm
• B cm
• C cm
• D 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 , 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 , find the mass of the sphere.

Q22:

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

Q23:

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

Work out a formula for in terms of .

• A
• B
• C
• D
• E

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 .

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

Q25:

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