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
25 filled with 102948 mℓ of water. The height of the water level in Container U is 1 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 29 cm.
- What is the capacity of Container U in litres?
- What is the volume of water in the container now in litres?
(a)
25 of Container U = 102948 mℓ
15 of Container U = 102948 ÷ 2 = 51474 mℓ
55 of Container U = 51474 x 5 = 257370 mℓ
1 ℓ = 1000 mℓ
Capacity of Container U = 257370 mℓ = 257.37 ℓ
(b)
Fraction of Container U not filled
= 1 -
25 =
35 Height of Container U not filled
=
35 x 70 cm
= 42 cm
Height of Container T
= 70 - 42 - 1
= 27 cm
Volume of remaining water in Container T
= 27 x 27 x 29
= 21141 cm
3 Volume of remaining water in Container U
= 70 x 70 x 29
= 142100 cm
3 Total volume of remaining water in the container
= 21141 + 142100
= 163241 cm
3
1 ℓ = 1000 cm
3 163241 cm
3 = 163.241 ℓ
Answer(s): (a) 257.37 ℓ; (b) 163.241 ℓ