The figure, not drawn to scale, is made of two connected cubical containers, M and N. Container M is sealed at the top and completely filled to the brim. Container N is
23 filled with 103728 mℓ of water. The height of the water level in Container N is 3 cm higher than that in Container M. Height of Container N is 61 cm. Water is then drained from the container and the height of the water level from the base falls to 27 cm.
- What is the capacity of Container N in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container N = 103728 mℓ
13 of Container N = 103728 ÷ 2 = 51864 mℓ
33 of Container N = 51864 x 3 = 155592 mℓ
1 ℓ = 1000 mℓ
Capacity of Container N = 155592 mℓ = 155.592 ℓ
(b)
Fraction of Container N not filled
= 1 -
23 =
13 Height of Container N not filled
=
13 x 61 cm
= 20.333333333333 cm
Height of Container M
= 61 - 20.333333333333 - 3
= 37.666666666667 cm
Volume of remaining water in Container M
= 37.666666666667 x 37.666666666667 x 27
= 38307.000000001 cm
3 Volume of remaining water in Container N
= 61 x 61 x 27
= 100467 cm
3 Total volume of remaining water in the container
= 38307.000000001 + 100467
= 138774 cm
3
1 ℓ = 1000 cm
3 138774 cm
3 = 138.774 ℓ
Answer(s): (a) 155.592 ℓ; (b) 138.774 ℓ