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5.04 Volume of cylinders and cones

Worksheet
Volume of cylinders
1

Find the volume of the following cylinders. Round your answers to one decimal place.

a
b
c
d
e
2

Find the volume of the following cylinders. Round your answers to one decimal place.

a

A cylinder with a radius of 6 \text{ cm} and height of 15 \text{ cm}.

b

A cylinder with a radius of 7 \text{ cm} and height of 15 \text{ cm}.

c

A cylinder with a diameter of 2 \text{ cm} and height of 19 \text{ cm}.

3

Find the volume of the following concrete cylindrical pipes. Round your answers to two decimal places.

a
b
c
4

Find the volume of the following solids. Round your answers to two decimal places.

a
b
c
d
e
5

The following solid is 3\text{ cm} thick. Calculate the volume of the solid correct to one decimal place.

6

Consider a cylinder with a diameter of 14 \text{ cm} and height of 10 \text{ cm}.

a

Find the volume of the cylinder in cubic centimetres, rounded to one decimal place.

b

State the capacity of the cylinder in millilitres, rounded to one decimal place.

7

If the radius of a cylinder is 8 \text{ cm} and its height is 18 \text{ cm}, find the amount of water it can hold in litres. Round your answer to two decimal places.

Volume of cones
8

Find the volume of the following cones. Round your answers to two decimal places.

a
b
9

Find the volume of the following cones. Round your answers to one decimal place.

a
b
10

A cone is sliced in half to produce the solid shown on the right. Find the volume of the solid. Round your answer to two decimal places.

11

Find the volume of the following cones. Round your answers to two decimal places.

a

A cone with a radius of 8 \text{ cm} and vertical height of 13 \text{ cm}.

b

A cone with a radius of 60 \text{ m} and a vertical height of 27.54 \text{ m}.

12

Consider the cone on the right:

a

Calculate the perpendicular height.

b

Hence find the volume of the cone. Round your answer to three significant figures.

13

Consider the following cone:

a

Find the volume of the cone in cubic centimetres. Round your answer to two decimal places.

b

Find the capacity of the cone in millilitres. Round your answer to two decimal places.

14

Consider the following cone:

a

Find the volume of the cone to the nearest cubic metre.

b

Find its capacity to the nearest litre.

15

Find the radius, r, of the following cones. Round your answers to two decimal places.

a

A cone with a volume of 1273.39 \text{ mm}^{3} and height of 19 \text{ mm}.

b

A cone with a volume of 196 \text{ mm}^{3} and height and radius of equal lengths.

16

Find the height, h, of a cone that has a volume of 603.19 \text{ m}^{3} and radius of 6 \text{ m}.

17

Consider the following net of a cone:

a

Which line segment has a length of 18 \text{ cm}?

b

Which line segment has a length of 30 \text{ cm}?

c

Find the perpendicular height, h, of the cone.

d

Find the volume of the cone in cubic centimetres. Round your answer to the nearest cubic centimetre.

18

The top of a solid cone was sawed off to form the solid shown on the right. Find the volume of the solid formed. Round your answer to two decimal places.

Applications
19

There are two types of cylindrical soup cans available for Bob to purchase at his local store. The first has a diameter of 16 \text{ cm} and a height of 18 \text{ cm}, and the second has a diameter of 18 \text{ cm} and a height of 16 \text{ cm}.

State which type of can holds more soup, the first can or the second can.

20

A cylindrical swimming pool has a diameter of 5\text{ m} and a depth of 1.8\text{ m}.

a

How many litres of water can the pool contain? Round your answer to the nearest litre.

b

Express this amount of water in kilolitres.

21

About how many litres of water can this water cooler bottle contain? Round your answer to one decimal place.

22

Jack's mother told him to drink 3 large bottles of water each day. She gave him a cylindrical bottle with height 17\text{ cm} and radius 5\text{ cm}.

a

Find the volume of the bottle. Round your answer to two decimal places.

b

Assuming that he drinks 3 full bottles as his mother suggested, calculate the volume of water Jack drinks each day. Round your answer to two decimal places.

c

If Jack follows this drinking routine for a week, how many litres of water would he drink altogether? Round your answer to the nearest litre.

23

A wedding cake with three tiers is shown. The layers have radii of 51\text{ cm}, 55\text{ cm} and 59\text{ cm}.

If each layer is 20\text{ cm} high, calculate the total volume of the cake in cubic metres. Round your answer to two decimal places.

24

A hollow cylindrical pipe has the dimensions shown in the figure:

a

Calculate the volume of the pipe, correct to two decimal places.

b

The pipe is made of metal where 1\text{ cm}^{3} of the metal weighs 5.7\text{ g}.

Calculate the weight of the pipe to one decimal place.

25

A theatre serves popcorn in a small conical container and a large cylindrical container as shown below:

a

How many small containers must be purchased in order to have the same amount of popcorn as in the large container?

b

Find the volume of the smaller container in cubic centimetres. Round your answer to the nearest cubic centimetre.

c

Find the volume of the larger container in cubic centimetres. Round your answer to the nearest cubic centimetre.

d

The cost of a small container of popcorn is \$1.30 and the cost of a large container of popcorn is \$3.50. Which is the better buy?

26

Before 1980, Mount St. Helens was a volcano approximately in the shape of the top cone below:

a

What was the volume of the mountain, in cubic kilometres? Round your answer to two decimal places.

b

The tip of the mountain was in the shape of the bottom cone shown.

Find the volume of the tip in cubic kilometres. Round your answer to two decimal places.

c

In 1980, Mount St. Helens erupted and the tip was destroyed.

Find the volume of the remaining mountain, in cubic kilometres. Round your answer to two decimal places.

27

A cylindrical tank with diameter of 3\text{ m} is placed in a 2 \text{ m} deep circular hole so that there is a gap of 40\text{ cm} between the side of the tank and the hole. The top of the tank is level with the ground.

a

What volume of dirt was removed to make the hole? Give your answer to the nearest cubic metre.

b

Find the capacity of the tank to the nearest litre.

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Outcomes

MS11-4

performs calculations in relation to two-dimensional and three-dimensional figures

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