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
23 filled with 115412 mℓ of water. The height of the water level in Container W is 5 cm higher than that in Container V. Height of Container W is 57 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 W in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container W = 115412 mℓ
13 of Container W = 115412 ÷ 2 = 57706 mℓ
33 of Container W = 57706 x 3 = 173118 mℓ
1 ℓ = 1000 mℓ
Capacity of Container W = 173118 mℓ = 173.118 ℓ
(b)
Fraction of Container W not filled
= 1 -
23 =
13 Height of Container W not filled
=
13 x 57 cm
= 19 cm
Height of Container V
= 57 - 19 - 5
= 33 cm
Volume of remaining water in Container V
= 33 x 33 x 31
= 33759 cm
3 Volume of remaining water in Container W
= 57 x 57 x 31
= 100719 cm
3 Total volume of remaining water in the container
= 33759 + 100719
= 134478 cm
3
1 ℓ = 1000 cm
3 134478 cm
3 = 134.478 ℓ
Answer(s): (a) 173.118 ℓ; (b) 134.478 ℓ