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
35 filled with 115833 mℓ of water. The height of the water level in Container C is 4 cm higher than that in Container B. Height of Container C is 60 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 C in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container C = 115833 mℓ
15 of Container C = 115833 ÷ 3 = 38611 mℓ
55 of Container C = 38611 x 5 = 193055 mℓ
1 ℓ = 1000 mℓ
Capacity of Container C = 193055 mℓ = 193.055 ℓ
(b)
Fraction of Container C not filled
= 1 -
35 =
25 Height of Container C not filled
=
25 x 60 cm
= 24 cm
Height of Container B
= 60 - 24 - 4
= 32 cm
Volume of remaining water in Container B
= 32 x 32 x 36
= 36864 cm
3 Volume of remaining water in Container C
= 60 x 60 x 36
= 129600 cm
3 Total volume of remaining water in the container
= 36864 + 129600
= 166464 cm
3
1 ℓ = 1000 cm
3 166464 cm
3 = 166.464 ℓ
Answer(s): (a) 193.055 ℓ; (b) 166.464 ℓ