The figure, not drawn to scale, is made of two connected cubical containers, M and N. Container M is sealed at the top and completely filled to the brim. Container N is
23 filled with 100662 mℓ of water. The height of the water level in Container N is 4 cm higher than that in Container M. Height of Container N is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 31 cm.
- What is the capacity of Container N in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container N = 100662 mℓ
13 of Container N = 100662 ÷ 2 = 50331 mℓ
33 of Container N = 50331 x 3 = 150993 mℓ
1 ℓ = 1000 mℓ
Capacity of Container N = 150993 mℓ = 150.993 ℓ
(b)
Fraction of Container N not filled
= 1 -
23 =
13 Height of Container N not filled
=
13 x 60 cm
= 20 cm
Height of Container M
= 60 - 20 - 4
= 36 cm
Volume of remaining water in Container M
= 36 x 36 x 31
= 40176 cm
3 Volume of remaining water in Container N
= 60 x 60 x 31
= 111600 cm
3 Total volume of remaining water in the container
= 40176 + 111600
= 151776 cm
3
1 ℓ = 1000 cm
3 151776 cm
3 = 151.776 ℓ
Answer(s): (a) 150.993 ℓ; (b) 151.776 ℓ