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
45 filled with 193744 mℓ of water. The height of the water level in Container D is 3 cm higher than that in Container C. Height of Container D is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 29 cm.
- What is the capacity of Container D in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container D = 193744 mℓ
15 of Container D = 193744 ÷ 4 = 48436 mℓ
55 of Container D = 48436 x 5 = 242180 mℓ
1 ℓ = 1000 mℓ
Capacity of Container D = 242180 mℓ = 242.18 ℓ
(b)
Fraction of Container D not filled
= 1 -
45 =
15 Height of Container D not filled
=
15 x 65 cm
= 13 cm
Height of Container C
= 65 - 13 - 3
= 49 cm
Volume of remaining water in Container C
= 49 x 49 x 29
= 69629 cm
3 Volume of remaining water in Container D
= 65 x 65 x 29
= 122525 cm
3 Total volume of remaining water in the container
= 69629 + 122525
= 192154 cm
3
1 ℓ = 1000 cm
3 192154 cm
3 = 192.154 ℓ
Answer(s): (a) 242.18 ℓ; (b) 192.154 ℓ