The figure, not drawn to scale, is made of two connected cubical containers, V and W. Container V is sealed at the top and completely filled to the brim. Container W is
23 filled with 117496 mℓ of water. The height of the water level in Container W is 3 cm higher than that in Container V. Height of Container W is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 27 cm.
- What is the capacity of Container W in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container W = 117496 mℓ
13 of Container W = 117496 ÷ 2 = 58748 mℓ
33 of Container W = 58748 x 3 = 176244 mℓ
1 ℓ = 1000 mℓ
Capacity of Container W = 176244 mℓ = 176.244 ℓ
(b)
Fraction of Container W not filled
= 1 -
23 =
13 Height of Container W not filled
=
13 x 70 cm
= 23.333333333333 cm
Height of Container V
= 70 - 23.333333333333 - 3
= 43.666666666667 cm
Volume of remaining water in Container V
= 43.666666666667 x 43.666666666667 x 27
= 51483.000000001 cm
3 Volume of remaining water in Container W
= 70 x 70 x 27
= 132300 cm
3 Total volume of remaining water in the container
= 51483.000000001 + 132300
= 183783 cm
3
1 ℓ = 1000 cm
3 183783 cm
3 = 183.783 ℓ
Answer(s): (a) 176.244 ℓ; (b) 183.783 ℓ