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5.051 Prisms and cylinders

Worksheet
Surface area of prisms
1

Find the surface area of the following cube with a side length of 6\text{ cm}:

2

Find the surface area of a cube with a side length of 4\text{ cm}.

3

Consider the following rectangular prism with length, width and height equal to 12\text{ m}, 6\text{ m} and 4\text{ m} respectively.

Find the surface area of the prism.

4

Find the surface area of a rectangular prism with dimensions: 4\text{ cm} by 9\text{ cm} by 8\text{ cm}

5

Find the surface area of the following triangular prisms:

a
b
6

For each of the following triangular prisms:

i

Find the value of x.

ii

Find the surface area.

a
b
7

Find the surface area of the following trapezoidal prisms:

a
b
8

Consider the following prism:

a

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

b

Find the surface area, correct to one decimal place.

9

Consider the following trapezoidal prism:

a

Find the value of y, correct to two decimal places.

b

Find the surface area, correct to one decimal place.

Surface area of cylinders
10

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

a
b
11

Find the surface area of the following cylinders using their given measurements. Round your answers to two decimal places.

a

Radius=5\text{ cm}, Height=7\text{ cm}

b

Radius=11\text{ m}, Height=8\text{ m}

c

Radius=20\text{ mm}, Height=20\text{ mm}

d

Radius=7.3\text{ cm}, Height=4.9\text{ cm}

e

Diameter=22\text{ mm}, Height=5\text{ mm}

f

Diameter=11.2\text{ cm}, Height=21.8\text{ cm}

12

Find the exact surface area of a cylinder with diameter 6\text{ cm} and height 21\text{ cm}, leaving your answer in terms of \pi.

13

A cylindrical can of radius 7\text{ cm} and height 10\text{ cm} is open at one end. Find the external surface area of the can, correct to two decimal places.

14

A hollow cylinderical tube has a radius of 3\text{ cm} and a length of 120\text{ cm}. Find the exact external surface area of the tube, leaving your answer in terms of \pi.

Volume of prisms
15

Find the volume of the following boxes:

a

A box is 1 \text{ m} long, 20 \text{ cm} high and 30\text{ cm} wide.

b

A box is 2\text{ m} long, 40\text{ cm} high and 50\text{ cm} wide.

16

Find the volume of the following prisms:

a
b
c
d
e
f
17

The roof of a cottage has the shape of a triangular prism with the dimensions shown below.

Find the volume of the roof.

18

Find the volume of the following tent in cubic metres:

Volume of cylinders
19

Find the volume of a cylinder with diameter 2\text{ cm} and a height of 19\text{ cm}. Round your answer to one decimal place.

20

Find the exact volume of the following cylinders using their given measurements, leaving your answers in terms of \pi.

a

Radius=2\text{ cm}, Height=7\text{ cm}

b

Radius=6\text{ cm}, Height=5\text{ cm}

c

Diameter=12\text{ mm}, Height=4\text{ mm}

d

Diameter=1.8\text{ m}, Height=0.7\text{ m}

21

Find the volume of the following solids, rounding your answers to one decimal place:

a
b
22

A cylinder has an exact volume of 216\pi\text{ units}^3. Find a pair of possible values for the radius and height of the cylinder.

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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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