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 166696 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 63 cm. Water is then drained from the container and the height of the water level from the base falls to 28 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 = 166696 mℓ
13 of Container H = 166696 ÷ 2 = 83348 mℓ
33 of Container H = 83348 x 3 = 250044 mℓ
1 ℓ = 1000 mℓ
Capacity of Container H = 250044 mℓ = 250.044 ℓ
(b)
Fraction of Container H not filled
= 1 -
23 =
13 Height of Container H not filled
=
13 x 63 cm
= 21 cm
Height of Container G
= 63 - 21 - 2
= 40 cm
Volume of remaining water in Container G
= 40 x 40 x 28
= 44800 cm
3 Volume of remaining water in Container H
= 63 x 63 x 28
= 111132 cm
3 Total volume of remaining water in the container
= 44800 + 111132
= 155932 cm
3
1 ℓ = 1000 cm
3 155932 cm
3 = 155.932 ℓ
Answer(s): (a) 250.044 ℓ; (b) 155.932 ℓ