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 103876 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 55 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 = 103876 mℓ
13 of Container H = 103876 ÷ 2 = 51938 mℓ
33 of Container H = 51938 x 3 = 155814 mℓ
1 ℓ = 1000 mℓ
Capacity of Container H = 155814 mℓ = 155.814 ℓ
(b)
Fraction of Container H not filled
= 1 -
23 =
13 Height of Container H not filled
=
13 x 55 cm
= 18.333333333333 cm
Height of Container G
= 55 - 18.333333333333 - 2
= 34.666666666667 cm
Volume of remaining water in Container G
= 34.666666666667 x 34.666666666667 x 27
= 32448.000000001 cm
3 Volume of remaining water in Container H
= 55 x 55 x 27
= 81675 cm
3 Total volume of remaining water in the container
= 32448.000000001 + 81675
= 114123 cm
3
1 ℓ = 1000 cm
3 114123 cm
3 = 114.123 ℓ
Answer(s): (a) 155.814 ℓ; (b) 114.123 ℓ