The figure, not drawn to scale, is made of two connected cubical containers, B and C. Container B is sealed at the top and completely filled to the brim. Container C is
45 filled with 116136 mℓ of water. The height of the water level in Container C is 3 cm higher than that in Container B. Height of Container C is 57 cm. Water is then drained from the container and the height of the water level from the base falls to 25 cm.
- What is the capacity of Container C in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container C = 116136 mℓ
15 of Container C = 116136 ÷ 4 = 29034 mℓ
55 of Container C = 29034 x 5 = 145170 mℓ
1 ℓ = 1000 mℓ
Capacity of Container C = 145170 mℓ = 145.17 ℓ
(b)
Fraction of Container C not filled
= 1 -
45 =
15 Height of Container C not filled
=
15 x 57 cm
= 11.4 cm
Height of Container B
= 57 - 11.4 - 3
= 42.6 cm
Volume of remaining water in Container B
= 42.6 x 42.6 x 25
= 45369 cm
3 Volume of remaining water in Container C
= 57 x 57 x 25
= 81225 cm
3 Total volume of remaining water in the container
= 45369 + 81225
= 126594 cm
3
1 ℓ = 1000 cm
3 126594 cm
3 = 126.594 ℓ
Answer(s): (a) 145.17 ℓ; (b) 126.594 ℓ