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 109176 mℓ of water. The height of the water level in Container V is 5 cm higher than that in Container U. Height of Container V 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 V in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container V = 109176 mℓ
15 of Container V = 109176 ÷ 3 = 36392 mℓ
55 of Container V = 36392 x 5 = 181960 mℓ
1 ℓ = 1000 mℓ
Capacity of Container V = 181960 mℓ = 181.96 ℓ
(b)
Fraction of Container V not filled
= 1 -
35 =
25 Height of Container V not filled
=
25 x 60 cm
= 24 cm
Height of Container U
= 60 - 24 - 5
= 31 cm
Volume of remaining water in Container U
= 31 x 31 x 30
= 28830 cm
3 Volume of remaining water in Container V
= 60 x 60 x 30
= 108000 cm
3 Total volume of remaining water in the container
= 28830 + 108000
= 136830 cm
3
1 ℓ = 1000 cm
3 136830 cm
3 = 136.83 ℓ
Answer(s): (a) 181.96 ℓ; (b) 136.83 ℓ