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
23 filled with 144858 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 63 cm. Water is then drained from the container and the height of the water level from the base falls to 27 cm.
- What is the capacity of Container P in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container P = 144858 mℓ
13 of Container P = 144858 ÷ 2 = 72429 mℓ
33 of Container P = 72429 x 3 = 217287 mℓ
1 ℓ = 1000 mℓ
Capacity of Container P = 217287 mℓ = 217.287 ℓ
(b)
Fraction of Container P not filled
= 1 -
23 =
13 Height of Container P not filled
=
13 x 63 cm
= 21 cm
Height of Container N
= 63 - 21 - 3
= 39 cm
Volume of remaining water in Container N
= 39 x 39 x 27
= 41067 cm
3 Volume of remaining water in Container P
= 63 x 63 x 27
= 107163 cm
3 Total volume of remaining water in the container
= 41067 + 107163
= 148230 cm
3
1 ℓ = 1000 cm
3 148230 cm
3 = 148.23 ℓ
Answer(s): (a) 217.287 ℓ; (b) 148.23 ℓ