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
45 filled with 163716 mℓ of water. The height of the water level in Container X is 3 cm higher than that in Container W. Height of Container X is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 31 cm.
- What is the capacity of Container X in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container X = 163716 mℓ
15 of Container X = 163716 ÷ 4 = 40929 mℓ
55 of Container X = 40929 x 5 = 204645 mℓ
1 ℓ = 1000 mℓ
Capacity of Container X = 204645 mℓ = 204.645 ℓ
(b)
Fraction of Container X not filled
= 1 -
45 =
15 Height of Container X not filled
=
15 x 65 cm
= 13 cm
Height of Container W
= 65 - 13 - 3
= 49 cm
Volume of remaining water in Container W
= 49 x 49 x 31
= 74431 cm
3 Volume of remaining water in Container X
= 65 x 65 x 31
= 130975 cm
3 Total volume of remaining water in the container
= 74431 + 130975
= 205406 cm
3
1 ℓ = 1000 cm
3 205406 cm
3 = 205.406 ℓ
Answer(s): (a) 204.645 ℓ; (b) 205.406 ℓ