Worksheet: Finding the Volume of a Sphere

Q1:

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

• A
• B
• C
• D
• E

Q2:

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

Q3:

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

• A 166.25 cm3
• B 785.55 cm3
• C 498.76 cm3
• D cm3
• E 261.85 cm3

Q4:

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

Q5:

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

Q6:

What is the volume of a sphere whose diameter is 6?

• A
• B
• C 288
• D
• E

Q7:

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

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:

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

Q10:

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

Q11:

Find the radius of a sphere whose volume is cm3.

• A cm
• B cm
• C cm
• D cm

Q12:

Find the radius of a sphere whose volume is 3 052.08 cm3. (Use ).

Q13:

Find the diameter of a sphere whose volume is 33.49 cm3. (Take ).

Q14:

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

Q15:

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

Q16:

A cube has a volume of 9 261 cubic inches. Find, to the nearest tenth, the volume of the circumscribed sphere of the cube.

Q17:

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

Q18:

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?

Q19:

David makes an ice cream cone with two spherical scoops of ice cream. Before he has time to eat the ice cream it melts and fills the cone up to the very top. Given that the cone has an internal height of 14 cm and an internal radius of 3 cm, what is the radius of a scoop of ice cream?

• A cm
• B cm
• C cm
• D cm
• E cm

Q20:

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 , find the radius of the sphere formed.

• A 90 cm
• B cm
• C cm
• D 42 cm
• E 46 cm

Q21:

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.

• A 22 cm
• B 7 cm
• C 28 cm
• D 9 cm

Q22:

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.

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

Q23:

A sphere with a radius of 10 feet has a density of 8 lb/ft3. Work out, to the nearest pound, the mass of the sphere, knowing that density .

Q24:

Earth has a mass of lb and a radius of miles. By modeling Earth as a perfect sphere, work out its density to the nearest pound per cubic foot, knowing that density .

Q25:

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.