The figure, not drawn to scale, is made of two connected cubical containers, T and U. Container T is sealed at the top and completely filled to the brim. Container U is
45 filled with 117176 mℓ of water. The height of the water level in Container U is 4 cm higher than that in Container T. Height of Container U is 70 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 U in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container U = 117176 mℓ
15 of Container U = 117176 ÷ 4 = 29294 mℓ
55 of Container U = 29294 x 5 = 146470 mℓ
1 ℓ = 1000 mℓ
Capacity of Container U = 146470 mℓ = 146.47 ℓ
(b)
Fraction of Container U not filled
= 1 -
45 =
15 Height of Container U not filled
=
15 x 70 cm
= 14 cm
Height of Container T
= 70 - 14 - 4
= 52 cm
Volume of remaining water in Container T
= 52 x 52 x 30
= 81120 cm
3 Volume of remaining water in Container U
= 70 x 70 x 30
= 147000 cm
3 Total volume of remaining water in the container
= 81120 + 147000
= 228120 cm
3
1 ℓ = 1000 cm
3 228120 cm
3 = 228.12 ℓ
Answer(s): (a) 146.47 ℓ; (b) 228.12 ℓ