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 124916 mℓ of water. The height of the water level in Container Y is 1 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 25 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 = 124916 mℓ
13 of Container Y = 124916 ÷ 2 = 62458 mℓ
33 of Container Y = 62458 x 3 = 187374 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Y = 187374 mℓ = 187.374 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 - 1
= 41 cm
Volume of remaining water in Container X
= 41 x 41 x 25
= 42025 cm
3 Volume of remaining water in Container Y
= 63 x 63 x 25
= 99225 cm
3 Total volume of remaining water in the container
= 42025 + 99225
= 141250 cm
3
1 ℓ = 1000 cm
3 141250 cm
3 = 141.25 ℓ
Answer(s): (a) 187.374 ℓ; (b) 141.25 ℓ