UNIT CONVERSION PROBLEMS ON SURFACE AREA AND VOLUME

Fill in :

Problem 1 :

1 m³ = 1 m × 1 m × 1 m

1 m³ = 100 cm × _____ × _____

1 m³ = _____ cm³

Solution :

1 m³ = 100 cm × 100 cm × 100 cm

1 m³ = 10,00000 cm³

So, 1 m³ is equal to 10,00000 cm³.

Problem 2 :

Use your answer to part (a) to convert these volumes to the units shown :

i) 4 m³ to cm³           ii) 7.5 m³ to cm³

iii) 250,000 cm³ to m³           iv) 32,000 cm³ to m³

Solution :

i) 1 m³ = 10,00000 cm³

4 m³ = 4 × 1000000

= 4000000 cm³

So, 4 m³ is equal to 4000000 cm³.

ii) 1 m³ = 10,00000 cm³

7.5 m³ = 7.5 × 1000000

= 7500000 cm³

So, 7.5 m³ is equal to 7500000 cm³.

iii) 1 cm³ = (1/1000000)m³

250,000 cm³ = (250000/1000000) m³

= 0.25 m³

So, 250,000 cm³ is equal to 0.25 m³.

iv) 1 cm³ = (1/1000000)m³

32,000 cm³ = (32,000/1000000) m³

= 0.032 m³

So, 32,000 cm³ is equal to 0.032 m³.

Problem 3 :

A rectangular tank of water has a square base of side 1.75 m. It can be filled with water up to a maximum height of 1.5 m. Work out in cubic metres, the maximum volume of water that this tank can hold. Give your answer correct to 2 decimal places.

Solution ;

length = 1.75 m

width = 1.75 m

height = 1.5 m

Volume = length × width × height

= 1.75 × 1.75 × 1.5

= 4.59 m³

So, maximum volume of water that this tank can hold is 4.59 m³.

Problem 4 :

Mrs Jones is tiling her kitchen floor. Each kitchen tile measures 20 cm by 20 cm. The floor measures 3m wide and 5m long.

The tiles are sold in boxes of 10. Each box costs £6.

Work out the total cost of the tiles needed for the kitchen floor.

Solution :

wide = 3 m

length = 5 m

Each box costs = £6.

since,1 m = 100 cm

3 m = 300 cm

5 m = 500 cm

= (300 × 500)/(20 × 20)

= 150000/400

= 375 pcs

The tiles are sold in boxes of 10.

= 375/10

= 37.5

= 38 boxes

= 38 × 6

= £228

So, the total cost of the tiles needed for the kitchen floor is £228.

Problem 5 :

Shown below is a fish tank.

Calculate how many litres of water are needed to fill an empty fish tank.

Solution :

Volume rectangle tank = length × width × height

= 60 × 15 × 10

= 9000 cm³

1 cm³ = 0.001 litres

9000 cm³ = 9000 × 0.001

= 9 litres

So, 9 litres of water are needed to fill an empty fish tank.

Problem 6 :

Shown below is a rectangle.

(a) Find the area of the rectangle in m².

(b) Find the area of the rectangle in cm². 

Solution :

(a) Area of the rectangle = l × w

length = 4 m

width = 2 m

= 4 × 2

= 8 m²

(b) Area of the rectangle = l × w

length = 4 m

width = 2 m

since,1 m = 100 cm

4 m = 400 cm

2 m = 200 cm

= 400 × 200

= 80000 cm²

Problem 7 :

Shown below is a cube.

(a) Find the volume of the cube in m³.

(b) Find the volume of the volume in cm³.

Solution :

(a)  volume of the cube = a³

a = 2 m

= 2³

= 8 m³

(b)  volume of the cube = a³

a = 2 m

1 m = 100 cm

2 m = 200 cm

= (200)³

= 8000000 cm³

Problem 8 :

Shown below are three containers of water. The amounts of water in each is shown.

List the containers in order, from least water to greatest water.

Solution :

1 cm³ = 0.001 litres

350 cm³ = 350 × 0.001

350 cm³  = 0.35 litres

1 litres = 1000 ml

0.35 litres = 0.35 × 1000

0.35 litres = 350 ml

1 litres = 1000 ml

0.08 litres = 0.8 × 1000

0.08 litres  = 800 ml

Least water to greatest water = 0.08 litres, 400 ml and 350 cm³.