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Worksheet: Volumes of Spheres

Q1:

Find the diameter of a sphere whose volume is 113.04 cm3. (Take πœ‹ = 3 . 1 4 ).

Q2:

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

  • A 7 7 7 6 πœ‹ cm3
  • B 2 4 3 πœ‹ cm3
  • C 7 2 9 πœ‹ cm3
  • D 9 7 2 πœ‹ cm3
  • E 2 7 πœ‹ cm3

Q3:

The radius of a sphere is 3 √ 7 0 8 cm. Find its volume in terms of πœ‹ .

Q4:

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

  • A 3 6 0 0 0 πœ‹
  • B 3 0 0 πœ‹
  • C 36 000
  • D 4 5 0 0 πœ‹
  • E 1 3 5 0 0 πœ‹

Q5:

Find the edge length of the smallest cube in which a sphere of volume 2 3 0 4 πœ‹ cm3 fits.

Q6:

Three-quarters of the volume of a sphere is 7 2 9 πœ‹ cm3. What is the radius of the sphere?

Q7:

A sphere with a volume of 2 3 0 4 πœ‹ cm3 is placed inside a cube. Given that it touches all six of the cube’s faces, find the volume of the cube.

  • A 144 cm3
  • B 1 728 cm3
  • C 576 cm3
  • D 13 824 cm3

Q8:

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

Q9:

A cylindrical tank with a radius of 3 feet is partially filled with water. A spherical ball with a radius of 2 feet is dropped into the tank. Assuming that the sphere is completely submerged and the cylindrical tank does not overflow, find the height, β„Ž , by which the water level rises. Give your answer to two decimal places.

Q10:

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

  • A 𝑉 = πœ‹ π‘Ÿ β„Ž 2
  • B 𝑉 = 1 3 πœ‹ π‘Ÿ β„Ž 2
  • C 𝑉 = πœ‹ π‘Ÿ β„Ž 2
  • D 𝑉 = 4 3 πœ‹ π‘Ÿ 3
  • E 𝑉 = 4 3 πœ‹ π‘Ÿ 2

Q11:

Find the radius of a sphere whose volume is 1 375 357.68 cm3. (Use πœ‹ = 3 . 1 4 ).

Q12:

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 2 9 cm
  • C 2 3 cm
  • D 8 2 7 cm

Q13:

Find, to the nearest tenth, the volume of a sphere given that the area of its great circle is 4 0 0 πœ‹ in2.

Q14:

Find, to the nearest tenth, the volume of a sphere given that the circumference of its great circle is 9 0 πœ‹ in.

Q15:

Find the radius of a sphere whose volume is cm3.

  • A cm
  • B cm
  • C cm
  • D cm

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:

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 ο„ž 2 1 8 cm
  • B 3 2 ο„ž 7 2 cm
  • C 3 √ 7 2 3 cm
  • D 3 ο„ž 6 3 4 cm
  • E 3 √ 6 3 2 cm

Q18:

Find the volume of a sphere whose diameter is 4.2 cm. Use πœ‹ = 2 2 7 .

Q19:

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œ‹ = 2 2 7 , find the mass of the sphere.

  • A 1 339 g
  • B 606 g
  • C 1 340 g
  • D 605 g
  • E 341 g

Q20:

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 1 0 4 7 . 3 9 cm3
  • E 261.85 cm3

Q21:

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

Q22:

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

Q23:

Two spheres have volumes of 1 6 2 πœ‹ and 3 0 7 2 πœ‹ cubic centimeters. What is the ratio of the radius of the small sphere to that of the large one?

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

Q24:

The volume, 𝑉 , of a sphere in terms of its radius, π‘Ÿ , is given by 𝑉 ( π‘Ÿ ) = 4 3 πœ‹ π‘Ÿ 3 . Express π‘Ÿ 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 π‘Ÿ = ο„ž 3 𝑉 4 πœ‹ 3 , 16.7 feet
  • B π‘Ÿ = ο„ž 4 𝑉 3 πœ‹ 3 , 4.4 feet
  • C π‘Ÿ = ο„ž 4 𝑉 3 πœ‹ 3 , 20.2 feet
  • D π‘Ÿ = ο„ž 3 𝑉 4 πœ‹ 3 , 3.6 feet
  • E π‘Ÿ = ο„ž 3 𝑉 4 πœ‹ , 6.9 feet

Q25:

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