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 187530 mℓ of water. The height of the water level in Container C is 5 cm higher than that in Container B. Height of Container C is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 35 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 = 187530 mℓ
15 of Container C = 187530 ÷ 3 = 62510 mℓ
55 of Container C = 62510 x 5 = 312550 mℓ
1 ℓ = 1000 mℓ
Capacity of Container C = 312550 mℓ = 312.55 ℓ
(b)
Fraction of Container C not filled
= 1 -
35 =
25 Height of Container C not filled
=
25 x 70 cm
= 28 cm
Height of Container B
= 70 - 28 - 5
= 37 cm
Volume of remaining water in Container B
= 37 x 37 x 35
= 47915 cm
3 Volume of remaining water in Container C
= 70 x 70 x 35
= 171500 cm
3 Total volume of remaining water in the container
= 47915 + 171500
= 219415 cm
3
1 ℓ = 1000 cm
3 219415 cm
3 = 219.415 ℓ
Answer(s): (a) 312.55 ℓ; (b) 219.415 ℓ