The figure, not drawn to scale, is made of two connected cubical containers, X and Y. Container X is sealed at the top and completely filled to the brim. Container Y is
23 filled with 128170 mℓ of water. The height of the water level in Container Y is 3 cm higher than that in Container X. Height of Container Y is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 40 cm.
- What is the capacity of Container Y in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container Y = 128170 mℓ
13 of Container Y = 128170 ÷ 2 = 64085 mℓ
33 of Container Y = 64085 x 3 = 192255 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Y = 192255 mℓ = 192.255 ℓ
(b)
Fraction of Container Y not filled
= 1 -
23 =
13 Height of Container Y not filled
=
13 x 66 cm
= 22 cm
Height of Container X
= 66 - 22 - 3
= 41 cm
Volume of remaining water in Container X
= 41 x 41 x 40
= 67240 cm
3 Volume of remaining water in Container Y
= 66 x 66 x 40
= 174240 cm
3 Total volume of remaining water in the container
= 67240 + 174240
= 241480 cm
3
1 ℓ = 1000 cm
3 241480 cm
3 = 241.48 ℓ
Answer(s): (a) 192.255 ℓ; (b) 241.48 ℓ