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
25 filled with 104156 mℓ of water. The height of the water level in Container M is 3 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 33 cm.
- What is the capacity of Container M in litres?
- What is the volume of water in the container now in litres?
(a)
25 of Container M = 104156 mℓ
15 of Container M = 104156 ÷ 2 = 52078 mℓ
55 of Container M = 52078 x 5 = 260390 mℓ
1 ℓ = 1000 mℓ
Capacity of Container M = 260390 mℓ = 260.39 ℓ
(b)
Fraction of Container M not filled
= 1 -
25 =
35 Height of Container M not filled
=
35 x 70 cm
= 42 cm
Height of Container L
= 70 - 42 - 3
= 25 cm
Volume of remaining water in Container L
= 25 x 25 x 33
= 20625 cm
3 Volume of remaining water in Container M
= 70 x 70 x 33
= 161700 cm
3 Total volume of remaining water in the container
= 20625 + 161700
= 182325 cm
3
1 ℓ = 1000 cm
3 182325 cm
3 = 182.325 ℓ
Answer(s): (a) 260.39 ℓ; (b) 182.325 ℓ