The figure, not drawn to scale, is made of two connected cubical containers, A and B. Container A is sealed at the top and completely filled to the brim. Container B is
45 filled with 123748 mℓ of water. The height of the water level in Container B is 4 cm higher than that in Container A. Height of Container B is 60 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 B in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container B = 123748 mℓ
15 of Container B = 123748 ÷ 4 = 30937 mℓ
55 of Container B = 30937 x 5 = 154685 mℓ
1 ℓ = 1000 mℓ
Capacity of Container B = 154685 mℓ = 154.685 ℓ
(b)
Fraction of Container B not filled
= 1 -
45 =
15 Height of Container B not filled
=
15 x 60 cm
= 12 cm
Height of Container A
= 60 - 12 - 4
= 44 cm
Volume of remaining water in Container A
= 44 x 44 x 30
= 58080 cm
3 Volume of remaining water in Container B
= 60 x 60 x 30
= 108000 cm
3 Total volume of remaining water in the container
= 58080 + 108000
= 166080 cm
3
1 ℓ = 1000 cm
3 166080 cm
3 = 166.08 ℓ
Answer(s): (a) 154.685 ℓ; (b) 166.08 ℓ