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 145334 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 63 cm. Water is then drained from the container and the height of the water level from the base falls to 24 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 = 145334 mℓ
13 of Container D = 145334 ÷ 2 = 72667 mℓ
33 of Container D = 72667 x 3 = 218001 mℓ
1 ℓ = 1000 mℓ
Capacity of Container D = 218001 mℓ = 218.001 ℓ
(b)
Fraction of Container D not filled
= 1 -
23 =
13 Height of Container D not filled
=
13 x 63 cm
= 21 cm
Height of Container C
= 63 - 21 - 3
= 39 cm
Volume of remaining water in Container C
= 39 x 39 x 24
= 36504 cm
3 Volume of remaining water in Container D
= 63 x 63 x 24
= 95256 cm
3 Total volume of remaining water in the container
= 36504 + 95256
= 131760 cm
3
1 ℓ = 1000 cm
3 131760 cm
3 = 131.76 ℓ
Answer(s): (a) 218.001 ℓ; (b) 131.76 ℓ