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
45 filled with 185184 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 70 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)
45 of Container E = 185184 mℓ
15 of Container E = 185184 ÷ 4 = 46296 mℓ
55 of Container E = 46296 x 5 = 231480 mℓ
1 ℓ = 1000 mℓ
Capacity of Container E = 231480 mℓ = 231.48 ℓ
(b)
Fraction of Container E not filled
= 1 -
45 =
15 Height of Container E not filled
=
15 x 70 cm
= 14 cm
Height of Container D
= 70 - 14 - 3
= 53 cm
Volume of remaining water in Container D
= 53 x 53 x 25
= 70225 cm
3 Volume of remaining water in Container E
= 70 x 70 x 25
= 122500 cm
3 Total volume of remaining water in the container
= 70225 + 122500
= 192725 cm
3
1 ℓ = 1000 cm
3 192725 cm
3 = 192.725 ℓ
Answer(s): (a) 231.48 ℓ; (b) 192.725 ℓ