The figure, not drawn to scale, is made of two connected cubical containers, N and P. Container N is sealed at the top and completely filled to the brim. Container P is
45 filled with 167108 mℓ of water. The height of the water level in Container P is 3 cm higher than that in Container N. Height of Container P is 70 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 P in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container P = 167108 mℓ
15 of Container P = 167108 ÷ 4 = 41777 mℓ
55 of Container P = 41777 x 5 = 208885 mℓ
1 ℓ = 1000 mℓ
Capacity of Container P = 208885 mℓ = 208.885 ℓ
(b)
Fraction of Container P not filled
= 1 -
45 =
15 Height of Container P not filled
=
15 x 70 cm
= 14 cm
Height of Container N
= 70 - 14 - 3
= 53 cm
Volume of remaining water in Container N
= 53 x 53 x 22
= 61798 cm
3 Volume of remaining water in Container P
= 70 x 70 x 22
= 107800 cm
3 Total volume of remaining water in the container
= 61798 + 107800
= 169598 cm
3
1 ℓ = 1000 cm
3 169598 cm
3 = 169.598 ℓ
Answer(s): (a) 208.885 ℓ; (b) 169.598 ℓ