The figure, not drawn to scale, is made of two connected cubical containers, L and M. Container L is sealed at the top and completely filled to the brim. Container M is
35 filled with 176766 mℓ of water. The height of the water level in Container M is 5 cm higher than that in Container L. Height of Container M is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 39 cm.
- What is the capacity of Container M in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container M = 176766 mℓ
15 of Container M = 176766 ÷ 3 = 58922 mℓ
55 of Container M = 58922 x 5 = 294610 mℓ
1 ℓ = 1000 mℓ
Capacity of Container M = 294610 mℓ = 294.61 ℓ
(b)
Fraction of Container M not filled
= 1 -
35 =
25 Height of Container M not filled
=
25 x 70 cm
= 28 cm
Height of Container L
= 70 - 28 - 5
= 37 cm
Volume of remaining water in Container L
= 37 x 37 x 39
= 53391 cm
3 Volume of remaining water in Container M
= 70 x 70 x 39
= 191100 cm
3 Total volume of remaining water in the container
= 53391 + 191100
= 244491 cm
3
1 ℓ = 1000 cm
3 244491 cm
3 = 244.491 ℓ
Answer(s): (a) 294.61 ℓ; (b) 244.491 ℓ