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
23 filled with 155086 mℓ of water. The height of the water level in Container Y is 3 cm higher than that in Container X. Height of Container Y is 62 cm. Water is then drained from the container and the height of the water level from the base falls to 36 cm.
- What is the capacity of Container Y in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container Y = 155086 mℓ
13 of Container Y = 155086 ÷ 2 = 77543 mℓ
33 of Container Y = 77543 x 3 = 232629 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Y = 232629 mℓ = 232.629 ℓ
(b)
Fraction of Container Y not filled
= 1 -
23 =
13 Height of Container Y not filled
=
13 x 62 cm
= 20.666666666667 cm
Height of Container X
= 62 - 20.666666666667 - 3
= 38.333333333333 cm
Volume of remaining water in Container X
= 38.333333333333 x 38.333333333333 x 36
= 52899.999999999 cm
3 Volume of remaining water in Container Y
= 62 x 62 x 36
= 138384 cm
3 Total volume of remaining water in the container
= 52899.999999999 + 138384
= 191284 cm
3
1 ℓ = 1000 cm
3 191284 cm
3 = 191.284 ℓ
Answer(s): (a) 232.629 ℓ; (b) 191.284 ℓ