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 178688 mℓ of water. The height of the water level in Container E is 2 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 22 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 = 178688 mℓ
13 of Container E = 178688 ÷ 2 = 89344 mℓ
33 of Container E = 89344 x 3 = 268032 mℓ
1 ℓ = 1000 mℓ
Capacity of Container E = 268032 mℓ = 268.032 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 - 2
= 44 cm
Volume of remaining water in Container D
= 44 x 44 x 22
= 42592 cm
3 Volume of remaining water in Container E
= 69 x 69 x 22
= 104742 cm
3 Total volume of remaining water in the container
= 42592 + 104742
= 147334 cm
3
1 ℓ = 1000 cm
3 147334 cm
3 = 147.334 ℓ
Answer(s): (a) 268.032 ℓ; (b) 147.334 ℓ