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
34 filled with 111672 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 68 cm. Water is then drained from the container and the height of the water level from the base falls to 38 cm.
- What is the capacity of Container U in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container U = 111672 mℓ
14 of Container U = 111672 ÷ 3 = 37224 mℓ
44 of Container U = 37224 x 4 = 148896 mℓ
1 ℓ = 1000 mℓ
Capacity of Container U = 148896 mℓ = 148.896 ℓ
(b)
Fraction of Container U not filled
= 1 -
34 =
14 Height of Container U not filled
=
14 x 68 cm
= 17 cm
Height of Container T
= 68 - 17 - 5
= 46 cm
Volume of remaining water in Container T
= 46 x 46 x 38
= 80408 cm
3 Volume of remaining water in Container U
= 68 x 68 x 38
= 175712 cm
3 Total volume of remaining water in the container
= 80408 + 175712
= 256120 cm
3
1 ℓ = 1000 cm
3 256120 cm
3 = 256.12 ℓ
Answer(s): (a) 148.896 ℓ; (b) 256.12 ℓ