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 186512 mℓ of water. The height of the water level in Container P is 1 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 20 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 = 186512 mℓ
15 of Container P = 186512 ÷ 4 = 46628 mℓ
55 of Container P = 46628 x 5 = 233140 mℓ
1 ℓ = 1000 mℓ
Capacity of Container P = 233140 mℓ = 233.14 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 - 1
= 55 cm
Volume of remaining water in Container N
= 55 x 55 x 20
= 60500 cm
3 Volume of remaining water in Container P
= 70 x 70 x 20
= 98000 cm
3 Total volume of remaining water in the container
= 60500 + 98000
= 158500 cm
3
1 ℓ = 1000 cm
3 158500 cm
3 = 158.5 ℓ
Answer(s): (a) 233.14 ℓ; (b) 158.5 ℓ