VOLUME  CONVERSION CHART

Problem 1 :

Calculate the capacity of the container:

Solution :

Length = 30 cm, width = 10 cm and height = 20 cm

Volume of container = length x width x height

= 30 x 10 x 20

= 6000 cm³

1 cm³ = 1 ml

= 6000 ml

1000 ml = 1 l

Capacity = 6000 / 1000

= 6 liter

Problem 2 :

Find the capacity in litres of a fishtank 2 m by 1 m by 50 cm.

Solution :

Length = 2 m ==> 200 cm

width = 1 m ==> 100 cm

height = 50 cm

Volume of container = length x width x height

= 200 x 100 x 50

= 1000000 cm³

= 1000000 ml

1000 ml = 1 l

= 1000000/1000

= 1000 l

Problem 3 :

A container is 20 cm by 10 cm by 10 cm. Find:

a) the volume of space in the container in cm³

b) the capacity of the container in mL

c) the capacity of the container in litres.

Solution :

Length = 20 cm, width = 10 cm and height = 10 cm

Volume = length x width x height

= 20 x 10 x 10

= 2000 cm³

a) the volume of space in the container in cm³

Volume of container in cm³ is 2000 cm³

b) the capacity of the container in mL

1 cm³ = 1 ml

Capacity of container in ml = 2000 ml

c) the capacity of the container in litres.

1 l = 1000 ml

2 l = 2000 ml

Capacity of container in liter is 2 l.

Problem 4 :

A rectangular container has dimensions 8 cm by 7 cm by 20 cm. Find its capacity in L.

Solution :

Length = 8 cm, width = 7 cm and height = 20 cm

Volume of container in cm³ = length x width x height

= 8 x 7 x 20

= 1120 cm³

= 1120 ml

1 liter = 1000 ml

= 1120/1000

= 1.120 liter

So, the required capacity is 1.12 liter.

Problem 5 :

A rectangular water tank has dimensions 4 m by 4 m by 2 m. Find its capacity in kL. 

Solution :

length = 4 m, width = 4 m and height = 2 m

Volume of rectangular tank = length x width x height

= 4 x 4 x 2

= 32 m³

1 m³ = 1 kl

= 32 kl

So, the capacity of water tank is 32 kl.

Problem 6 :

A rectangular petrol tank has dimensions 50 cm by 40 cm by 25 cm. How many litres of petrol are needed to fill it?

Solution :

length = 50 cm, width = 40 cm and height = 25 cm

Volume of rectangular tank = length x width x height

= 50 x 40 x 25

= 50000 cm³

1 cm³ = 1 ml

= 50000 ml

= 5000/1000

= 5 liter

So, the capacity of rectangular tank is 5 liter.

Problem 7 :

water trough has triangular cross-section as shown. Its length is 2 m.

Find :

a) the area of the triangle in cm²

b) the volume of space in the trough in cm³

c) the capacity of the trough in:

i) litres    ii) kilolitres.

Solution :

Volume of the prism = base area x height

base area = (1/2) x base x height

= (1/2) x 60 x 50

= 30 x 50

= 1500 cm²

height = 2 m = 200 cm

Volume = 1500 x 200

= 300000 cm³

a) the area of the triangle is 1500 cm²

b) the volume of space in the trough is 300000 cm³

c) the capacity of the trough in:

1 liter = 1000 ml

1 cm³ = 1 ml

i) litres

300000 cm³ = 300000 ml

= 300000/1000

= 300 l

ii) kilolitres

1 kiliter = 1000 liter

1 liter = 1/1000 kl

= 300/1000

= 0.3 kl

Problem 8 :

A rectangular tank with a base measuring 2.4 m by 1.2 m has water in it to a height of 1 m. If the level water is increased by 20 cm, how many more liters are now in the tank ?

Solution :

length = 2.4 m, width = 1.2 m and height = 20 cm ==> 0.2 m

Volume = 2.4 x 1.2 x 0.2

= 0.576 m³

= 0.576 x 1000

= 576 liter

So, additional volume of water is 576 liter.

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