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
23 filled with 111170 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 69 cm. Water is then drained from the container and the height of the water level from the base falls to 26 cm.
- What is the capacity of Container C in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container C = 111170 mℓ
13 of Container C = 111170 ÷ 2 = 55585 mℓ
33 of Container C = 55585 x 3 = 166755 mℓ
1 ℓ = 1000 mℓ
Capacity of Container C = 166755 mℓ = 166.755 ℓ
(b)
Fraction of Container C not filled
= 1 -
23 =
13 Height of Container C not filled
=
13 x 69 cm
= 23 cm
Height of Container B
= 69 - 23 - 4
= 42 cm
Volume of remaining water in Container B
= 42 x 42 x 26
= 45864 cm
3 Volume of remaining water in Container C
= 69 x 69 x 26
= 123786 cm
3 Total volume of remaining water in the container
= 45864 + 123786
= 169650 cm
3
1 ℓ = 1000 cm
3 169650 cm
3 = 169.65 ℓ
Answer(s): (a) 166.755 ℓ; (b) 169.65 ℓ