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 111654 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 67 cm. Water is then drained from the container and the height of the water level from the base falls to 27 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 = 111654 mℓ
13 of Container Y = 111654 ÷ 2 = 55827 mℓ
33 of Container Y = 55827 x 3 = 167481 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Y = 167481 mℓ = 167.481 ℓ
(b)
Fraction of Container Y not filled
= 1 -
23 =
13 Height of Container Y not filled
=
13 x 67 cm
= 22.333333333333 cm
Height of Container X
= 67 - 22.333333333333 - 2
= 42.666666666667 cm
Volume of remaining water in Container X
= 42.666666666667 x 42.666666666667 x 27
= 49152.000000001 cm
3 Volume of remaining water in Container Y
= 67 x 67 x 27
= 121203 cm
3 Total volume of remaining water in the container
= 49152.000000001 + 121203
= 170355 cm
3
1 ℓ = 1000 cm
3 170355 cm
3 = 170.355 ℓ
Answer(s): (a) 167.481 ℓ; (b) 170.355 ℓ