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
35 filled with 139332 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 65 cm. Water is then drained from the container and the height of the water level from the base falls to 34 cm.
- What is the capacity of Container U in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container U = 139332 mℓ
15 of Container U = 139332 ÷ 3 = 46444 mℓ
55 of Container U = 46444 x 5 = 232220 mℓ
1 ℓ = 1000 mℓ
Capacity of Container U = 232220 mℓ = 232.22 ℓ
(b)
Fraction of Container U not filled
= 1 -
35 =
25 Height of Container U not filled
=
25 x 65 cm
= 26 cm
Height of Container T
= 65 - 26 - 1
= 38 cm
Volume of remaining water in Container T
= 38 x 38 x 34
= 49096 cm
3 Volume of remaining water in Container U
= 65 x 65 x 34
= 143650 cm
3 Total volume of remaining water in the container
= 49096 + 143650
= 192746 cm
3
1 ℓ = 1000 cm
3 192746 cm
3 = 192.746 ℓ
Answer(s): (a) 232.22 ℓ; (b) 192.746 ℓ