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
25 filled with 129860 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 70 cm. Water is then drained from the container and the height of the water level from the base falls to 32 cm.
- What is the capacity of Container W in litres?
- What is the volume of water in the container now in litres?
(a)
25 of Container W = 129860 mℓ
15 of Container W = 129860 ÷ 2 = 64930 mℓ
55 of Container W = 64930 x 5 = 324650 mℓ
1 ℓ = 1000 mℓ
Capacity of Container W = 324650 mℓ = 324.65 ℓ
(b)
Fraction of Container W not filled
= 1 -
25 =
35 Height of Container W not filled
=
35 x 70 cm
= 42 cm
Height of Container V
= 70 - 42 - 1
= 27 cm
Volume of remaining water in Container V
= 27 x 27 x 32
= 23328 cm
3 Volume of remaining water in Container W
= 70 x 70 x 32
= 156800 cm
3 Total volume of remaining water in the container
= 23328 + 156800
= 180128 cm
3
1 ℓ = 1000 cm
3 180128 cm
3 = 180.128 ℓ
Answer(s): (a) 324.65 ℓ; (b) 180.128 ℓ