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 127677 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 65 cm. Water is then drained from the container and the height of the water level from the base falls to 30 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 = 127677 mℓ
15 of Container M = 127677 ÷ 3 = 42559 mℓ
55 of Container M = 42559 x 5 = 212795 mℓ
1 ℓ = 1000 mℓ
Capacity of Container M = 212795 mℓ = 212.795 ℓ
(b)
Fraction of Container M not filled
= 1 -
35 =
25 Height of Container M not filled
=
25 x 65 cm
= 26 cm
Height of Container L
= 65 - 26 - 4
= 35 cm
Volume of remaining water in Container L
= 35 x 35 x 30
= 36750 cm
3 Volume of remaining water in Container M
= 65 x 65 x 30
= 126750 cm
3 Total volume of remaining water in the container
= 36750 + 126750
= 163500 cm
3
1 ℓ = 1000 cm
3 163500 cm
3 = 163.5 ℓ
Answer(s): (a) 212.795 ℓ; (b) 163.5 ℓ