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
35 filled with 120270 mℓ of water. The height of the water level in Container W is 1 cm higher than that in Container V. Height of Container W is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 30 cm.
- What is the capacity of Container W in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container W = 120270 mℓ
15 of Container W = 120270 ÷ 3 = 40090 mℓ
55 of Container W = 40090 x 5 = 200450 mℓ
1 ℓ = 1000 mℓ
Capacity of Container W = 200450 mℓ = 200.45 ℓ
(b)
Fraction of Container W not filled
= 1 -
35 =
25 Height of Container W not filled
=
25 x 65 cm
= 26 cm
Height of Container V
= 65 - 26 - 1
= 38 cm
Volume of remaining water in Container V
= 38 x 38 x 30
= 43320 cm
3 Volume of remaining water in Container W
= 65 x 65 x 30
= 126750 cm
3 Total volume of remaining water in the container
= 43320 + 126750
= 170070 cm
3
1 ℓ = 1000 cm
3 170070 cm
3 = 170.07 ℓ
Answer(s): (a) 200.45 ℓ; (b) 170.07 ℓ