The figure, not drawn to scale, is made of two connected cubical containers, W and X. Container W is sealed at the top and completely filled to the brim. Container X is
23 filled with 132040 mℓ of water. The height of the water level in Container X is 4 cm higher than that in Container W. Height of Container X is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 39 cm.
- What is the capacity of Container X in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container X = 132040 mℓ
13 of Container X = 132040 ÷ 2 = 66020 mℓ
33 of Container X = 66020 x 3 = 198060 mℓ
1 ℓ = 1000 mℓ
Capacity of Container X = 198060 mℓ = 198.06 ℓ
(b)
Fraction of Container X not filled
= 1 -
23 =
13 Height of Container X not filled
=
13 x 60 cm
= 20 cm
Height of Container W
= 60 - 20 - 4
= 36 cm
Volume of remaining water in Container W
= 36 x 36 x 39
= 50544 cm
3 Volume of remaining water in Container X
= 60 x 60 x 39
= 140400 cm
3 Total volume of remaining water in the container
= 50544 + 140400
= 190944 cm
3
1 ℓ = 1000 cm
3 190944 cm
3 = 190.944 ℓ
Answer(s): (a) 198.06 ℓ; (b) 190.944 ℓ