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 173988 mℓ of water. The height of the water level in Container H is 2 cm higher than that in Container G. Height of Container H is 67 cm. Water is then drained from the container and the height of the water level from the base falls to 27 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 = 173988 mℓ
13 of Container H = 173988 ÷ 2 = 86994 mℓ
33 of Container H = 86994 x 3 = 260982 mℓ
1 ℓ = 1000 mℓ
Capacity of Container H = 260982 mℓ = 260.982 ℓ
(b)
Fraction of Container H not filled
= 1 -
23 =
13 Height of Container H not filled
=
13 x 67 cm
= 22.333333333333 cm
Height of Container G
= 67 - 22.333333333333 - 2
= 42.666666666667 cm
Volume of remaining water in Container G
= 42.666666666667 x 42.666666666667 x 27
= 49152.000000001 cm
3 Volume of remaining water in Container H
= 67 x 67 x 27
= 121203 cm
3 Total volume of remaining water in the container
= 49152.000000001 + 121203
= 170355 cm
3
1 ℓ = 1000 cm
3 170355 cm
3 = 170.355 ℓ
Answer(s): (a) 260.982 ℓ; (b) 170.355 ℓ