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
34 filled with 127419 mℓ of water. The height of the water level in Container Y is 4 cm higher than that in Container X. Height of Container Y is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 32 cm.
- What is the capacity of Container Y in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container Y = 127419 mℓ
14 of Container Y = 127419 ÷ 3 = 42473 mℓ
44 of Container Y = 42473 x 4 = 169892 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Y = 169892 mℓ = 169.892 ℓ
(b)
Fraction of Container Y not filled
= 1 -
34 =
14 Height of Container Y not filled
=
14 x 60 cm
= 15 cm
Height of Container X
= 60 - 15 - 4
= 41 cm
Volume of remaining water in Container X
= 41 x 41 x 32
= 53792 cm
3 Volume of remaining water in Container Y
= 60 x 60 x 32
= 115200 cm
3 Total volume of remaining water in the container
= 53792 + 115200
= 168992 cm
3
1 ℓ = 1000 cm
3 168992 cm
3 = 168.992 ℓ
Answer(s): (a) 169.892 ℓ; (b) 168.992 ℓ