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 118772 mℓ of water. The height of the water level in Container Y is 5 cm higher than that in Container X. Height of Container Y is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 37 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 = 118772 mℓ
13 of Container Y = 118772 ÷ 2 = 59386 mℓ
33 of Container Y = 59386 x 3 = 178158 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Y = 178158 mℓ = 178.158 ℓ
(b)
Fraction of Container Y not filled
= 1 -
23 =
13 Height of Container Y not filled
=
13 x 63 cm
= 21 cm
Height of Container X
= 63 - 21 - 5
= 37 cm
Volume of remaining water in Container X
= 37 x 37 x 37
= 50653 cm
3 Volume of remaining water in Container Y
= 63 x 63 x 37
= 146853 cm
3 Total volume of remaining water in the container
= 50653 + 146853
= 197506 cm
3
1 ℓ = 1000 cm
3 197506 cm
3 = 197.506 ℓ
Answer(s): (a) 178.158 ℓ; (b) 197.506 ℓ