The figure, not drawn to scale, is made of two connected cubical containers, X and Y. Container X is sealed at the top and completely filled to the brim. Container Y is
45 filled with 175640 mℓ of water. The height of the water level in Container Y is 2 cm higher than that in Container X. Height of Container Y is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 24 cm.
- What is the capacity of Container Y in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container Y = 175640 mℓ
15 of Container Y = 175640 ÷ 4 = 43910 mℓ
55 of Container Y = 43910 x 5 = 219550 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Y = 219550 mℓ = 219.55 ℓ
(b)
Fraction of Container Y not filled
= 1 -
45 =
15 Height of Container Y not filled
=
15 x 65 cm
= 13 cm
Height of Container X
= 65 - 13 - 2
= 50 cm
Volume of remaining water in Container X
= 50 x 50 x 24
= 60000 cm
3 Volume of remaining water in Container Y
= 65 x 65 x 24
= 101400 cm
3 Total volume of remaining water in the container
= 60000 + 101400
= 161400 cm
3
1 ℓ = 1000 cm
3 161400 cm
3 = 161.4 ℓ
Answer(s): (a) 219.55 ℓ; (b) 161.4 ℓ