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
23 filled with 137096 mℓ of water. The height of the water level in Container M is 4 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 36 cm.
- What is the capacity of Container M in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container M = 137096 mℓ
13 of Container M = 137096 ÷ 2 = 68548 mℓ
33 of Container M = 68548 x 3 = 205644 mℓ
1 ℓ = 1000 mℓ
Capacity of Container M = 205644 mℓ = 205.644 ℓ
(b)
Fraction of Container M not filled
= 1 -
23 =
13 Height of Container M not filled
=
13 x 70 cm
= 23.333333333333 cm
Height of Container L
= 70 - 23.333333333333 - 4
= 42.666666666667 cm
Volume of remaining water in Container L
= 42.666666666667 x 42.666666666667 x 36
= 65536.000000001 cm
3 Volume of remaining water in Container M
= 70 x 70 x 36
= 176400 cm
3 Total volume of remaining water in the container
= 65536.000000001 + 176400
= 241936 cm
3
1 ℓ = 1000 cm
3 241936 cm
3 = 241.936 ℓ
Answer(s): (a) 205.644 ℓ; (b) 241.936 ℓ