Worksheet: Surface Areas of Spheres

In this worksheet, we will practice using the formula for the surface area of a sphere in terms of its radius or diameter to find the sphere's area, radius, or diameter.

Q1:

Find the surface area of the given sphere to the nearest tenth.

Q2:

What is the diameter of a sphere whose surface area is 36𝜋 cm2?

Q3:

Find the total surface area of the hemisphere. Round the answer to the nearest tenth.

Q4:

Find the surface area of a sphere whose diameter is 12.6 cm. Use 𝜋=227.

Q5:

Find, to the nearest tenth, the surface area of a sphere whose great circle has a circumference of 140𝜋 ft.

Q6:

Find the surface area of a sphere to the nearest tenth if the area of the great circle is 441𝜋 in2.

Q7:

The diagram shows a cylinder of radius 𝑟 and height and a sphere of radius 𝑟.

The total surface area of the sphere is no less than that of the cylinder. Write an inequality connecting and 𝑟.

  • A < 𝑟
  • B > 𝑟
  • C 𝑟
  • D 𝑟
  • E 𝑟

Q8:

Given that the volume of a sphere is 562.5𝜋 cm3, find its surface area in terms of 𝜋.

  • A 5 6 . 2 5 𝜋 cm2
  • B 2 2 5 𝜋 cm2
  • C225 cm2
  • D56.25 cm2

Q9:

Find, to the nearest tenth, the curved surface area of a hemisphere, given that the area of the great circle is 441𝜋 mm2.

Q10:

Find, to the nearest tenth, the curved surface area of a hemisphere given that the circumference of its great circle is 4𝜋 cm.

Q11:

A water feature can be modelled as a hemisphere with its base set onto a square patio. If the diameter of the hemisphere is 4 feet and the patio has a side of length 6 feet, what would the visible area of the patio be? Give your answer accurate to two decimal places.

Q12:

Find the surface area of a sphere to the nearest tenth if the area of the great circle is 144𝜋 in2.

Q13:

Find, to the nearest tenth, the surface area of a sphere whose great circle has a circumference of 118𝜋 ft.

Q14:

Find the surface area of the given sphere to the nearest tenth.

Q15:

What is the diameter of a sphere whose surface area is 100𝜋 cm2?

Q16:

Given that the volume of a sphere is 121.5𝜋 cm3, find its surface area in terms of 𝜋.

  • A 2 0 . 2 5 𝜋 cm2
  • B 8 1 𝜋 cm2
  • C81 cm2
  • D20.25 cm2

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