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 157866 mℓ of water. The height of the water level in Container P is 5 cm higher than that in Container N. Height of Container P is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 30 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 = 157866 mℓ
13 of Container P = 157866 ÷ 2 = 78933 mℓ
33 of Container P = 78933 x 3 = 236799 mℓ
1 ℓ = 1000 mℓ
Capacity of Container P = 236799 mℓ = 236.799 ℓ
(b)
Fraction of Container P not filled
= 1 -
23 =
13 Height of Container P not filled
=
13 x 66 cm
= 22 cm
Height of Container N
= 66 - 22 - 5
= 39 cm
Volume of remaining water in Container N
= 39 x 39 x 30
= 45630 cm
3 Volume of remaining water in Container P
= 66 x 66 x 30
= 130680 cm
3 Total volume of remaining water in the container
= 45630 + 130680
= 176310 cm
3
1 ℓ = 1000 cm
3 176310 cm
3 = 176.31 ℓ
Answer(s): (a) 236.799 ℓ; (b) 176.31 ℓ