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
34 filled with 116721 mℓ of water. The height of the water level in Container P is 2 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 28 cm.
- What is the capacity of Container P in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container P = 116721 mℓ
14 of Container P = 116721 ÷ 3 = 38907 mℓ
44 of Container P = 38907 x 4 = 155628 mℓ
1 ℓ = 1000 mℓ
Capacity of Container P = 155628 mℓ = 155.628 ℓ
(b)
Fraction of Container P not filled
= 1 -
34 =
14 Height of Container P not filled
=
14 x 70 cm
= 17.5 cm
Height of Container N
= 70 - 17.5 - 2
= 50.5 cm
Volume of remaining water in Container N
= 50.5 x 50.5 x 28
= 71407 cm
3 Volume of remaining water in Container P
= 70 x 70 x 28
= 137200 cm
3 Total volume of remaining water in the container
= 71407 + 137200
= 208607 cm
3
1 ℓ = 1000 cm
3 208607 cm
3 = 208.607 ℓ
Answer(s): (a) 155.628 ℓ; (b) 208.607 ℓ