AustraliaNSW
Stage 5.1-3

# 7.03 Surface area of prisms and cylinders

Worksheet
Surface area of prisms
1

Find the surface area of the following prisms:

a
b
c
d
e
f
2

Consider the following rectangular prism:

a

Determine whether the following are the nets of this cube:

i
ii
iii
iv
b

Find the area of the prism's net.

c

Find the surface area of the rectangular prism.

3

What is the surface area of a cube with side length 4 \text{ cm}?

4

What is the side length of a cube that has a surface area of 384 \text{ cm }^2?

5

For each of the following triangular prisms:

i

Find the value of x.

ii

Find the surface area.

a
b
6

Find the surface area of the following trapezoidal prisms:

a
b
7

Consider the following prism:

a

Find the height, h, correct to two decimal places.

b

Find the surface area, correct to one decimal place.

8

Consider the following trapezoidal prism:

a

Find the value of y, rounded to one decimal place.

b

Find the surface area of the trapezoidal prism, rounded to one decimal place.

Surface area of cylinders
9

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

a
b
c
d
e
f
10

Consider the following cylinder:

a

Find the circumference of the circular base to four decimal places.

b

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

11

The area of the circular face on a cylinder is 8281 \pi \text{ m}^2. The total surface area of the cylinder is 25\,662 \pi \text{ m}^2

a

Find the radius of the cylinder.

b

Hence, find the height of the cylinder.

12

Find the height, h, of this closed cylinder if its surface area is 25\,547 \text{ m}^2 and the radius of its circular faces is 38 \text{ m}.

Applications
13

A birthday gift is placed inside the box shown, which has the shape of a rectangular prism.

Find the minimum amount of wrapping paper needed to cover this box.

14

The roof of a shed is the shape of a triangular prism with dimensions as shown in the diagram:

Find the surface area of the roof of the shed (do not include the base of the prism). Round your answer to the nearest square metre.

15

Laura is building a storage chest in the shape of a rectangular prism. The chest will be 55\text{ cm} long, 41\text{ cm} deep, and 39\text{ cm} high. Find the surface area of the chest.

16

A swimming pool has the shape of a trapezoidal prism 14\text{ m} long and 6 \text{ m} wide. The depth of the water ranges from 1.2\text{ m} to 2.5 \text{ m}, as shown in the diagram.

The walls and base of the pool are going to be tiled. Calculate the total area inside the pool that is to be tiled. Round your answer to one decimal place.

17

Find the surface area of the brickwork for this cylindrical silo. Assume that there is a brick roof but no floor.

18

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.

19

The diagram shows a water trough in the shape of a half cylinder:

Find the surface area of the outside of this water trough. Round your answer to two decimal places.

20

Both of the following popcorn bags are designed to carry 1680 \text{ cm} ^3 of popcorn. Assume there's minimal wastage of space when the popcorn is packed into each bag.

a

Find the height h of bag A in centimetres.

b

Find the height h of bag B in centimetres.

c

Find the surface area of bag A.

d

Find the surface area of bag B.

e

Which bag should be used to reduce the amount of paper?

21

Jenny 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 1683 \text{ cm}^2. Determine the number of complete cans can she make.

22

If two identical spherical balls with radii of 2.6 \text{ cm} fit exactly inside a cylinder, find the surface area of the closed cylinder. Round your answer to one decimal place.

23

A steel shed is to be constructed, with dimensions as shown below. The shed is to include a rectangular cut-out at the front for the entrance.

a

Determine the surface area of the shed. Round your answer to one decimal place.

b

Construction of the shed requires an additional 0.1\text{ m}^2 of sheet metal for each 1\text{ m}^2 of surface area, due to overlaps and wastage.

How much sheet metal is required to construct this shed? Round your answer up to the nearest square metre.

c

If the steel sheets cost \\$18 per square metre, calculate the total cost of the steel required to build this shed.