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
35 filled with 100368 mℓ of water. The height of the water level in Container E is 5 cm higher than that in Container D. Height of Container E is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 40 cm.
- What is the capacity of Container E in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container E = 100368 mℓ
15 of Container E = 100368 ÷ 3 = 33456 mℓ
55 of Container E = 33456 x 5 = 167280 mℓ
1 ℓ = 1000 mℓ
Capacity of Container E = 167280 mℓ = 167.28 ℓ
(b)
Fraction of Container E not filled
= 1 -
35 =
25 Height of Container E not filled
=
25 x 70 cm
= 28 cm
Height of Container D
= 70 - 28 - 5
= 37 cm
Volume of remaining water in Container D
= 37 x 37 x 40
= 54760 cm
3 Volume of remaining water in Container E
= 70 x 70 x 40
= 196000 cm
3 Total volume of remaining water in the container
= 54760 + 196000
= 250760 cm
3
1 ℓ = 1000 cm
3 250760 cm
3 = 250.76 ℓ
Answer(s): (a) 167.28 ℓ; (b) 250.76 ℓ