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 114388 mℓ of water. The height of the water level in Container U is 5 cm higher than that in Container T. Height of Container U is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 36 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 = 114388 mℓ
15 of Container U = 114388 ÷ 4 = 28597 mℓ
55 of Container U = 28597 x 5 = 142985 mℓ
1 ℓ = 1000 mℓ
Capacity of Container U = 142985 mℓ = 142.985 ℓ
(b)
Fraction of Container U not filled
= 1 -
45 =
15 Height of Container U not filled
=
15 x 65 cm
= 13 cm
Height of Container T
= 65 - 13 - 5
= 47 cm
Volume of remaining water in Container T
= 47 x 47 x 36
= 79524 cm
3 Volume of remaining water in Container U
= 65 x 65 x 36
= 152100 cm
3 Total volume of remaining water in the container
= 79524 + 152100
= 231624 cm
3
1 ℓ = 1000 cm
3 231624 cm
3 = 231.624 ℓ
Answer(s): (a) 142.985 ℓ; (b) 231.624 ℓ