The figure, not drawn to scale, is made of two connected cubical containers, G and H. Container G is sealed at the top and completely filled to the brim. Container H is
45 filled with 112380 mℓ of water. The height of the water level in Container H is 4 cm higher than that in Container G. Height of Container H is 65 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 H in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container H = 112380 mℓ
15 of Container H = 112380 ÷ 4 = 28095 mℓ
55 of Container H = 28095 x 5 = 140475 mℓ
1 ℓ = 1000 mℓ
Capacity of Container H = 140475 mℓ = 140.475 ℓ
(b)
Fraction of Container H not filled
= 1 -
45 =
15 Height of Container H not filled
=
15 x 65 cm
= 13 cm
Height of Container G
= 65 - 13 - 4
= 48 cm
Volume of remaining water in Container G
= 48 x 48 x 39
= 89856 cm
3 Volume of remaining water in Container H
= 65 x 65 x 39
= 164775 cm
3 Total volume of remaining water in the container
= 89856 + 164775
= 254631 cm
3
1 ℓ = 1000 cm
3 254631 cm
3 = 254.631 ℓ
Answer(s): (a) 140.475 ℓ; (b) 254.631 ℓ