The figure, not drawn to scale, is made of two connected cubical containers, L and M. Container L is sealed at the top and completely filled to the brim. Container M is
45 filled with 142580 mℓ of water. The height of the water level in Container M is 4 cm higher than that in Container L. Height of Container M is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 22 cm.
- What is the capacity of Container M in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container M = 142580 mℓ
15 of Container M = 142580 ÷ 4 = 35645 mℓ
55 of Container M = 35645 x 5 = 178225 mℓ
1 ℓ = 1000 mℓ
Capacity of Container M = 178225 mℓ = 178.225 ℓ
(b)
Fraction of Container M not filled
= 1 -
45 =
15 Height of Container M not filled
=
15 x 60 cm
= 12 cm
Height of Container L
= 60 - 12 - 4
= 44 cm
Volume of remaining water in Container L
= 44 x 44 x 22
= 42592 cm
3 Volume of remaining water in Container M
= 60 x 60 x 22
= 79200 cm
3 Total volume of remaining water in the container
= 42592 + 79200
= 121792 cm
3
1 ℓ = 1000 cm
3 121792 cm
3 = 121.792 ℓ
Answer(s): (a) 178.225 ℓ; (b) 121.792 ℓ