The figure, not drawn to scale, is made of two connected cubical containers, W and X. Container W is sealed at the top and completely filled to the brim. Container X is
25 filled with 124168 mℓ of water. The height of the water level in Container X is 2 cm higher than that in Container W. Height of Container X is 70 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 X in litres?
- What is the volume of water in the container now in litres?
(a)
25 of Container X = 124168 mℓ
15 of Container X = 124168 ÷ 2 = 62084 mℓ
55 of Container X = 62084 x 5 = 310420 mℓ
1 ℓ = 1000 mℓ
Capacity of Container X = 310420 mℓ = 310.42 ℓ
(b)
Fraction of Container X not filled
= 1 -
25 =
35 Height of Container X not filled
=
35 x 70 cm
= 42 cm
Height of Container W
= 70 - 42 - 2
= 26 cm
Volume of remaining water in Container W
= 26 x 26 x 25
= 16900 cm
3 Volume of remaining water in Container X
= 70 x 70 x 25
= 122500 cm
3 Total volume of remaining water in the container
= 16900 + 122500
= 139400 cm
3
1 ℓ = 1000 cm
3 139400 cm
3 = 139.4 ℓ
Answer(s): (a) 310.42 ℓ; (b) 139.4 ℓ