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1.05 Surface area of cylinders and spheres

Worksheet
Surface area of cylinders
1

For each of the following pairs of cylinders and their nets, find the curved surface area of the cylinder. Round your answers to two decimal places.

a
b
2

Consider the following cylinder together with its net:

a

Find the circumference of the circular base. Round your answers to four decimal places.

b

Hence, find the area of the curved face of the cylinder. Round your answers to two decimal places.

3

For each of the following cylinders:

i

Find the curved surface area of the cylinder. Round your answers to two decimal places.

ii

Find the total surface area of the cylinder. Round your answers to two decimal places.

a
b
4

Find the total surface area of each of the following cylinders. Round your answers to two decimal places.

a
b
c
d
5

Find the surface area of the following cylinders. Round your answers to two decimal places.

a
b
c
d
e
f
Surface area of spheres
6

Find the surface area of the following spheres. Round your answers to two decimal places.

a
b
c
d
e
f
g
7

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

a

A sphere with a radius of 8.2 \text{ mm}.

b

A sphere with a diameter of 6.8 \text{ cm}.

c

A sphere with a radius of 0.75 \text{ m}.

d

A sphere with a diameter of \dfrac{5}{3} \text{ cm}.

Applications
8

A cylindrical can of radius 7\text{ cm} and height 10\text{ cm} is open at one end. What is the external surface area of the can? Round your answer to two decimal places.

9

Ivan is using a toilet paper roll for crafts. He has measured the toilet paper roll to have a diameter 4 \text{ cm} and a length 10 \text{ cm}.

Find the surface area of the toilet paper roll. Round your answer to two decimal places.

10

Quiana wants to make several cans like the one shown. She plans to cut them out of a sheet of material that has an area of 1358 \text{ cm}^2.

How many complete cans can she make?

11

Find the surface area of the brickwork for this silo correct to two decimal places. Assume that there is a brick roof and no floor.

12

A paint roller is cylindrical in shape. It has a diameter of 6.8\text{ cm} and a width of 31.2\text{ cm}.

Find the area painted by the roller when it makes one revolution. Round your answer to two decimal places.

13

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

14

A cylindrical can of soup has a diameter of 5.4 \text{ cm} and a height of 8.6 \text{ cm}. The soup label fits perfectly around the curved surface of the can.

a

Find the area of the soup can's label. Round your answer to three decimal places.

b

If it costs \$0.03 per \text{cm}^2 to print a label, calculate the price of printing one soup can label.

c

Find the total price for the labels for a 24-can box of the soup.

15

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

a

A bowling ball has a radius of 10.9 \text{ cm}.

b

A softball has a diameter of 9.6 \text{ cm}.

16

The planet Jupiter has a radius of 69\,911 \text{ km}, and planet Venus has a radius of 6051.8 \text{ km}. Assuming both planets are spherical, how many times bigger is the surface area of Jupiter than Venus? Round your answer to one decimal place.

17

Two identical spherical balls with radii of 1.4 \text{ m} fit exactly inside a cylinder as shown. Find the surface area of the closed cylinder to one decimal place.

18

If a spherical ball with a radius of 3.7\text{ cm} fits exactly inside a cylinder, what is the surface area of the cylinder? Round your answer to one decimal place.

19

The Los Angeles Department of Water and Power released 96 million hollow black plastic balls onto the surface of a water reservoir to prevent evaporation and reduce algae growth. Each ball has a diameter of 10 centimetres.

a

Find the total surface area of all the balls, to the nearest square metre.

b

The plastic costs approximately \$11.44 per square metre to produce the balls. How much will cost to make all the balls? Give your answer in millions to one decimal place.

c

Approximately how much does each ball cost to produce, to the nearest cent?

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Outcomes

ACMEM095

find the surface area of familiar solids, including cubes, rectangular and triangular prisms, spheres and cylinders

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