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 123972 mℓ of water. The height of the water level in Container E is 3 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 25 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 = 123972 mℓ
13 of Container E = 123972 ÷ 2 = 61986 mℓ
33 of Container E = 61986 x 3 = 185958 mℓ
1 ℓ = 1000 mℓ
Capacity of Container E = 185958 mℓ = 185.958 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 - 3
= 43 cm
Volume of remaining water in Container D
= 43 x 43 x 25
= 46225 cm
3 Volume of remaining water in Container E
= 69 x 69 x 25
= 119025 cm
3 Total volume of remaining water in the container
= 46225 + 119025
= 165250 cm
3
1 ℓ = 1000 cm
3 165250 cm
3 = 165.25 ℓ
Answer(s): (a) 185.958 ℓ; (b) 165.25 ℓ