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
34 filled with 109524 mℓ of water. The height of the water level in Container N is 4 cm higher than that in Container M. Height of Container N is 62 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 N in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container N = 109524 mℓ
14 of Container N = 109524 ÷ 3 = 36508 mℓ
44 of Container N = 36508 x 4 = 146032 mℓ
1 ℓ = 1000 mℓ
Capacity of Container N = 146032 mℓ = 146.032 ℓ
(b)
Fraction of Container N not filled
= 1 -
34 =
14 Height of Container N not filled
=
14 x 62 cm
= 15.5 cm
Height of Container M
= 62 - 15.5 - 4
= 42.5 cm
Volume of remaining water in Container M
= 42.5 x 42.5 x 32
= 57800 cm
3 Volume of remaining water in Container N
= 62 x 62 x 32
= 123008 cm
3 Total volume of remaining water in the container
= 57800 + 123008
= 180808 cm
3
1 ℓ = 1000 cm
3 180808 cm
3 = 180.808 ℓ
Answer(s): (a) 146.032 ℓ; (b) 180.808 ℓ