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
23 filled with 101430 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 54 cm. Water is then drained from the container and the height of the water level from the base falls to 37 cm.
- What is the capacity of Container H in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container H = 101430 mℓ
13 of Container H = 101430 ÷ 2 = 50715 mℓ
33 of Container H = 50715 x 3 = 152145 mℓ
1 ℓ = 1000 mℓ
Capacity of Container H = 152145 mℓ = 152.145 ℓ
(b)
Fraction of Container H not filled
= 1 -
23 =
13 Height of Container H not filled
=
13 x 54 cm
= 18 cm
Height of Container G
= 54 - 18 - 4
= 32 cm
Volume of remaining water in Container G
= 32 x 32 x 37
= 37888 cm
3 Volume of remaining water in Container H
= 54 x 54 x 37
= 107892 cm
3 Total volume of remaining water in the container
= 37888 + 107892
= 145780 cm
3
1 ℓ = 1000 cm
3 145780 cm
3 = 145.78 ℓ
Answer(s): (a) 152.145 ℓ; (b) 145.78 ℓ