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
34 filled with 136830 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 64 cm. Water is then drained from the container and the height of the water level from the base falls to 35 cm.
- What is the capacity of Container W in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container W = 136830 mℓ
14 of Container W = 136830 ÷ 3 = 45610 mℓ
44 of Container W = 45610 x 4 = 182440 mℓ
1 ℓ = 1000 mℓ
Capacity of Container W = 182440 mℓ = 182.44 ℓ
(b)
Fraction of Container W not filled
= 1 -
34 =
14 Height of Container W not filled
=
14 x 64 cm
= 16 cm
Height of Container V
= 64 - 16 - 3
= 45 cm
Volume of remaining water in Container V
= 45 x 45 x 35
= 70875 cm
3 Volume of remaining water in Container W
= 64 x 64 x 35
= 143360 cm
3 Total volume of remaining water in the container
= 70875 + 143360
= 214235 cm
3
1 ℓ = 1000 cm
3 214235 cm
3 = 214.235 ℓ
Answer(s): (a) 182.44 ℓ; (b) 214.235 ℓ