The figure, not drawn to scale, is made of two connected cubical containers, P and Q. Container P is sealed at the top and completely filled to the brim. Container Q is
45 filled with 138388 mℓ of water. The height of the water level in Container Q is 5 cm higher than that in Container P. Height of Container Q is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 20 cm.
- What is the capacity of Container Q in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container Q = 138388 mℓ
15 of Container Q = 138388 ÷ 4 = 34597 mℓ
55 of Container Q = 34597 x 5 = 172985 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Q = 172985 mℓ = 172.985 ℓ
(b)
Fraction of Container Q not filled
= 1 -
45 =
15 Height of Container Q not filled
=
15 x 70 cm
= 14 cm
Height of Container P
= 70 - 14 - 5
= 51 cm
Volume of remaining water in Container P
= 51 x 51 x 20
= 52020 cm
3 Volume of remaining water in Container Q
= 70 x 70 x 20
= 98000 cm
3 Total volume of remaining water in the container
= 52020 + 98000
= 150020 cm
3
1 ℓ = 1000 cm
3 150020 cm
3 = 150.02 ℓ
Answer(s): (a) 172.985 ℓ; (b) 150.02 ℓ