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 132926 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 59 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 = 132926 mℓ
13 of Container P = 132926 ÷ 2 = 66463 mℓ
33 of Container P = 66463 x 3 = 199389 mℓ
1 ℓ = 1000 mℓ
Capacity of Container P = 199389 mℓ = 199.389 ℓ
(b)
Fraction of Container P not filled
= 1 -
23 =
13 Height of Container P not filled
=
13 x 59 cm
= 19.666666666667 cm
Height of Container N
= 59 - 19.666666666667 - 1
= 38.333333333333 cm
Volume of remaining water in Container N
= 38.333333333333 x 38.333333333333 x 27
= 39674.999999999 cm
3 Volume of remaining water in Container P
= 59 x 59 x 27
= 93987 cm
3 Total volume of remaining water in the container
= 39674.999999999 + 93987
= 133662 cm
3
1 ℓ = 1000 cm
3 133662 cm
3 = 133.662 ℓ
Answer(s): (a) 199.389 ℓ; (b) 133.662 ℓ