The figure, not drawn to scale, is made of two connected cubical containers, V and W. Container V is sealed at the top and completely filled to the brim. Container W is
45 filled with 108136 mℓ of water. The height of the water level in Container W is 3 cm higher than that in Container V. Height of Container W is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 20 cm.
- What is the capacity of Container W in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container W = 108136 mℓ
15 of Container W = 108136 ÷ 4 = 27034 mℓ
55 of Container W = 27034 x 5 = 135170 mℓ
1 ℓ = 1000 mℓ
Capacity of Container W = 135170 mℓ = 135.17 ℓ
(b)
Fraction of Container W not filled
= 1 -
45 =
15 Height of Container W not filled
=
15 x 70 cm
= 14 cm
Height of Container V
= 70 - 14 - 3
= 53 cm
Volume of remaining water in Container V
= 53 x 53 x 20
= 56180 cm
3 Volume of remaining water in Container W
= 70 x 70 x 20
= 98000 cm
3 Total volume of remaining water in the container
= 56180 + 98000
= 154180 cm
3
1 ℓ = 1000 cm
3 154180 cm
3 = 154.18 ℓ
Answer(s): (a) 135.17 ℓ; (b) 154.18 ℓ