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5.053 Spheres

Worksheet
Surface area of spheres and hemispheres
1

Find the surface area of the following spheres, correct to two decimal places:

a
b
2

Calculate the exact surface areas of the following spheres using their given measurements. Give your answers in terms of \pi.

a

Radius =2\text{ cm}

b

Radius =5\text{ cm}

c

Radius =\dfrac{3}{8}\text{ m}

d

Radius =14.9\text{ cm}

e

Diameter =10\text{ cm}

f

Diameter =23\text{ mm}

3

Find the surface area of the following hemisphere. Round your answer to three decimal places.

4

Calculate the exact surface areas of the following hemispheres using their given measurements. Give your answers in terms of \pi.

a

Radius =6\text{ m}

b

Radius =12\text{ cm}

c

Radius =22.7\text{ mm}

d

Diameter =7.4\text{ cm}

5

Calculate the surface area of a softball ball with a radius of 9.6\text{ cm}. Round your answer to two decimal places.

6

The planet Mars has a radius of 3390\text{ km}. Find the surface area of Mars, to the nearest whole number.

7

The planet Earth has a radius of 6370\text{ km}. Find the surface area of Earth.

8

The circumference of a golf ball is 4.2\pi\text{ cm}. Find the surface area of the ball.

Volume of spheres and hemispheres
9

If the radius of a sphere doubles, what happens to its volume?

10

Find the volume of the sphere shown.

Round your answer to two decimal places.

11

Calculate the exact volume of the spheres with the following radii. Give your answers in terms of \pi.

a

Radius =2\text{ m}

b

Radius =9\text{ cm}

c

Radius =30\text{ cm}

d

Radius =\dfrac{3}{4}\text{ m}

12

Find the volume of a bowling ball with a radius of 10.9\text{ cm}, correct to three decimal places.

13

The diameter of a tennis ball is 8.6\text{ cm}. Find the approximate volume of the ball, correct to two decimal places.

14

The volume of a sphere is 972 \pi \text{ yd}^3. Find the diameter of the sphere.

15

Find the volume of a hemisphere that has a radius of 12\text{ cm}. Round your answer to two decimal places.

16

The school canteen sells frozen half oranges. If the diameter of an orange is 76\text{ mm}, find the volume of one half orange. Round your answer to two decimal places.

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Outcomes

ACMGM019

calculate the volumes of standard three-dimensional objects such as spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations; for example, the volume of water contained in a swimming pool

ACMGM020

calculate the surface areas of standard three-dimensional objects such as spheres, rectangular prisms, cylinders, cones, pyramids and composites in practical situations; for example, the surface area of a cylindrical food container

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