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Middle Years

9.10 Volume and capacity

Worksheet
Capacity
1

Convert the following as specified:

a

68\,000 \, \text{mL} to L

b

52 \,\text{L} to mL

c

99\,000 \,\text{L} to kL

d

63 \,\text{kL} to L

e

1 \,\text {cm}^3 to mL

f

1 \,\text{mL} to \text{cm}^3

g

36 \,\text {cm}^3 to mL

h

720\,\text{mL} to \text{cm}^3

i

1 \,\text{m}^3 to kL

j

1 \,\text{kL} to \text{m}^3

k

83 \,\text{m}^3 to kL

l

270 \,\text{ kL} to \text{m}^3

m

0.4 \,\text{L} to mL

n

3.8 \,\text{mL} to L

o

1.67 \,\text{kL} to L

p

84.6 \,\text{ L} to kL

2

A prism has a volume of 74\,000\,\text{cm}^3. Find the capacity of the prism in litres.

3

A cylinder has a volume of 6100 \,\text{cm}^3. Find:

a

The capacity of the cylinder in millilitres.

b

The capacity of the cylinder in litres.

4

A rectangular prism has dimensions 30 \, \text{cm}, 78 \,\text{cm} and 9 \,\text{cm}.

a

Find the volume of the prism in cubic centimetres.

b
Hence, find the capacity of the prism in litres.
5

A container has a volume of 1 cubic metre. Find:

a

The capacity in millilitres.

b

The capacity in litres.

c

The capacity in kilolitres.

6

A rectangular prism has dimensions 3 \, \text{m}, 8 \,\text{m} and 6\,\text{m}.

a

Find the volume of the prism in cubic metres.

b
Hence, find the capacity of the prism in kilolitres.
7

A rectangular prism has dimensions 3 \, \text{m}, 7 \,\text{m} and 0.8\,\text{m}.

a
Find the volume of the prism in cubic metres.
b
Hence, find the capacity of the prism in litres.
8

A rectangular prism has dimensions 7 \, \text{cm}, 9 \,\text{cm} and 4 \,\text{cm} .

a
Find the volume of the prism in cubic centimetres.
b

Hence, find the capacity of the prism in millilitres.

9

A rectangular prism has dimensions 3 \, \text{cm}, 7 \,\text{cm} and 9 \,\text{cm}. Find the capacity of the prism in millilitres.

10

A rectangular prism has dimensions 40 \, \text{cm}, 900 \,\text{cm} and 7 \,\text{cm}. Find the capacity of the prism in litres.

11

A cylinder has a diameter of 8 \,\text{cm} and height of 7 \,\text{cm}.

a

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

b

Hence, find the capacity of the cylinder in millilitres, correct to one decimal place.

12

A cylinder has a diameter of 12 \,\text{cm} and height of 70 \,\text{cm}.

a

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

b

Hence, find the capacity of the cylinder in litres, correct to four decimal places.

13

A cylinder has a diameter of 6\,\text{m} and height of 7 \,\text{m}.

a

Find the volume of the cylinder in cubic metres, correct to one decimal place.

b

Hence, find the capacity of the cylinder in kilolitres, correct to one decimal place.

14

A cylinder has a diameter of 8 \,\text{m} and height of 90 \,\text{m}.

a

Find the volume of the cylinder in cubic metres, correct to four decimal places.

b
Hence, find the capacity of the cylinder in litres, correct to one decimal place.
15

A cylinder has a radius of 4 \,\text{cm} and height of 7 \,\text{cm}. Find the capacity of the cylinder in millilitres, correct to one decimal place.

16

A cylinder has a radius of 3 \,\text{cm} and height of 70 \,\text{cm}. Find the capacity of the cylinder in litres, correct to four decimal places.

Applications
17

James drank \dfrac{9}{10} \text{ L} of water. Find the amount that he drank in millilitres.

18

How many 150 \text{ mL} jugs of soda water will be needed to fill a 2.4 \text{ L} container?

19

Find the capacity of the fish tank in litres:

20

279 children went on a picnic. Each child drank 400 \text{ mL} of orange juice. How many litres were consumed altogether?

21

A tap is dripping at the rate of 4 \text{ mL} of water per minute. How many litres of water will be lost in one day?

22

A gravy boat is designed as a half-cylinder as shown. It has a diameter of 8\text{ cm} and a length of 15\text{ cm}.

Find its capacity to two decimal places.

23

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 metre cubed.

b

What is the capacity of the tank to the nearest litre?

24

A rectangular swimming pool has a length of 27 \text{ m}, width of 14 \text{ m} and depth of 3 \text{ m}.

a

Find the volume of this swimming pool in cubic metres.

b

Hence, find the capacity of the swimming pool in kilolitres.

25

Yvonne is designing a small cartridge. Its capacity must be exactly 10.4 millilitres. She has already finished designing the base, which will have an area of 13 square centimetres.

a

Find the volume of Yvonne's cartridge in cubic centimetres.

b

Assuming that Yvonne's cartridge is a prism, find its height in centimetres.

26

Nadia is designing a lava lamp. Its capacity must be exactly 4.8 litres. She has already finished designing the base, which will have an area of 120 square centimetres.

a

Find the volume of Nadia's lava lamp in cubic centimetres.

b

Assuming that Nadia's lamp is a triangular prism, find its height be in centimetres.

27

Kathleen is constructing a swimming pool designed to hold 34.4 kilolitres of water. She has already decided on a base area of 8 square metres.

a

Find the volume of Kathleen's pool in cubic metres.

b

If the depth of the pool is the same at every point, how deep must it be in metres.

28

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.

29

The swimming pool shown is composed of a trapezoidal prism joined to a half cylinder:

a

Find the volume of the pool in cubic metres. Round your answer to three decimal places.

b

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

c

If the pool is filled to a height 10\text{ cm} below the top, how many litres of water are in the pool? Round your answer to the nearest litre.

d

After construction works at a neighbouring property, a crack opens in the bottom of the pool and water begins to leak from the pool. It is observed that the height of the surface of the water in the pool is decreasing by 7\text{ cm} each week. Find the amount of water that is leaking out each week, to the nearest litre.

e

Assuming that water continues to leak at this rate, find how many whole weeks it will take to empty the pool.

30

Xavier has been hired by a live performance group that are famous for their strange and demanding requests. He must transport 228\,323 litres of edible slime from a production facility and deliver it to a nearby concert hall.

If even a single litre is missing, he will not be paid.

Xavier has a truck with a large, adjustable tank. The base of the tank has an area of 9.5 square metres, and to avoid collisions on his route the top of the tank must be no more than 3.94 metres from the base.

How many trips must Xavier make from the slime production facility to the concert hall?

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