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
23 filled with 142094 mℓ of water. The height of the water level in Container V is 3 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 24 cm.
- What is the capacity of Container V in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container V = 142094 mℓ
13 of Container V = 142094 ÷ 2 = 71047 mℓ
33 of Container V = 71047 x 3 = 213141 mℓ
1 ℓ = 1000 mℓ
Capacity of Container V = 213141 mℓ = 213.141 ℓ
(b)
Fraction of Container V not filled
= 1 -
23 =
13 Height of Container V not filled
=
13 x 60 cm
= 20 cm
Height of Container U
= 60 - 20 - 3
= 37 cm
Volume of remaining water in Container U
= 37 x 37 x 24
= 32856 cm
3 Volume of remaining water in Container V
= 60 x 60 x 24
= 86400 cm
3 Total volume of remaining water in the container
= 32856 + 86400
= 119256 cm
3
1 ℓ = 1000 cm
3 119256 cm
3 = 119.256 ℓ
Answer(s): (a) 213.141 ℓ; (b) 119.256 ℓ