The figure, not drawn to scale, is made of two connected cubical containers, D and E. Container D is sealed at the top and completely filled to the brim. Container E is
23 filled with 195530 mℓ of water. The height of the water level in Container E is 4 cm higher than that in Container D. Height of Container E is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 39 cm.
- What is the capacity of Container E in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container E = 195530 mℓ
13 of Container E = 195530 ÷ 2 = 97765 mℓ
33 of Container E = 97765 x 3 = 293295 mℓ
1 ℓ = 1000 mℓ
Capacity of Container E = 293295 mℓ = 293.295 ℓ
(b)
Fraction of Container E not filled
= 1 -
23 =
13 Height of Container E not filled
=
13 x 69 cm
= 23 cm
Height of Container D
= 69 - 23 - 4
= 42 cm
Volume of remaining water in Container D
= 42 x 42 x 39
= 68796 cm
3 Volume of remaining water in Container E
= 69 x 69 x 39
= 185679 cm
3 Total volume of remaining water in the container
= 68796 + 185679
= 254475 cm
3
1 ℓ = 1000 cm
3 254475 cm
3 = 254.475 ℓ
Answer(s): (a) 293.295 ℓ; (b) 254.475 ℓ