The figure, not drawn to scale, is made of two connected cubical containers, U and V. Container U is sealed at the top and completely filled to the brim. Container V is
35 filled with 106920 mℓ of water. The height of the water level in Container V is 2 cm higher than that in Container U. Height of Container V is 70 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 V in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container V = 106920 mℓ
15 of Container V = 106920 ÷ 3 = 35640 mℓ
55 of Container V = 35640 x 5 = 178200 mℓ
1 ℓ = 1000 mℓ
Capacity of Container V = 178200 mℓ = 178.2 ℓ
(b)
Fraction of Container V not filled
= 1 -
35 =
25 Height of Container V not filled
=
25 x 70 cm
= 28 cm
Height of Container U
= 70 - 28 - 2
= 40 cm
Volume of remaining water in Container U
= 40 x 40 x 25
= 40000 cm
3 Volume of remaining water in Container V
= 70 x 70 x 25
= 122500 cm
3 Total volume of remaining water in the container
= 40000 + 122500
= 162500 cm
3
1 ℓ = 1000 cm
3 162500 cm
3 = 162.5 ℓ
Answer(s): (a) 178.2 ℓ; (b) 162.5 ℓ