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
34 filled with 145497 mℓ of water. The height of the water level in Container Y is 4 cm higher than that in Container X. Height of Container Y is 61 cm. Water is then drained from the container and the height of the water level from the base falls to 32 cm.
- What is the capacity of Container Y in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container Y = 145497 mℓ
14 of Container Y = 145497 ÷ 3 = 48499 mℓ
44 of Container Y = 48499 x 4 = 193996 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Y = 193996 mℓ = 193.996 ℓ
(b)
Fraction of Container Y not filled
= 1 -
34 =
14 Height of Container Y not filled
=
14 x 61 cm
= 15.25 cm
Height of Container X
= 61 - 15.25 - 4
= 41.75 cm
Volume of remaining water in Container X
= 41.75 x 41.75 x 32
= 55778 cm
3 Volume of remaining water in Container Y
= 61 x 61 x 32
= 119072 cm
3 Total volume of remaining water in the container
= 55778 + 119072
= 174850 cm
3
1 ℓ = 1000 cm
3 174850 cm
3 = 174.85 ℓ
Answer(s): (a) 193.996 ℓ; (b) 174.85 ℓ