The figure, not drawn to scale, is made of two connected cubical containers, C and D. Container C is sealed at the top and completely filled to the brim. Container D is
23 filled with 113532 mℓ of water. The height of the water level in Container D is 1 cm higher than that in Container C. Height of Container D is 57 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 D in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container D = 113532 mℓ
13 of Container D = 113532 ÷ 2 = 56766 mℓ
33 of Container D = 56766 x 3 = 170298 mℓ
1 ℓ = 1000 mℓ
Capacity of Container D = 170298 mℓ = 170.298 ℓ
(b)
Fraction of Container D not filled
= 1 -
23 =
13 Height of Container D not filled
=
13 x 57 cm
= 19 cm
Height of Container C
= 57 - 19 - 1
= 37 cm
Volume of remaining water in Container C
= 37 x 37 x 22
= 30118 cm
3 Volume of remaining water in Container D
= 57 x 57 x 22
= 71478 cm
3 Total volume of remaining water in the container
= 30118 + 71478
= 101596 cm
3
1 ℓ = 1000 cm
3 101596 cm
3 = 101.596 ℓ
Answer(s): (a) 170.298 ℓ; (b) 101.596 ℓ