The figure, not drawn to scale, is made of two connected cubical containers, Y and Z. Container Y is sealed at the top and completely filled to the brim. Container Z is
23 filled with 191146 mℓ of water. The height of the water level in Container Z is 3 cm higher than that in Container Y. Height of Container Z is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 27 cm.
- What is the capacity of Container Z in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container Z = 191146 mℓ
13 of Container Z = 191146 ÷ 2 = 95573 mℓ
33 of Container Z = 95573 x 3 = 286719 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Z = 286719 mℓ = 286.719 ℓ
(b)
Fraction of Container Z not filled
= 1 -
23 =
13 Height of Container Z not filled
=
13 x 66 cm
= 22 cm
Height of Container Y
= 66 - 22 - 3
= 41 cm
Volume of remaining water in Container Y
= 41 x 41 x 27
= 45387 cm
3 Volume of remaining water in Container Z
= 66 x 66 x 27
= 117612 cm
3 Total volume of remaining water in the container
= 45387 + 117612
= 162999 cm
3
1 ℓ = 1000 cm
3 162999 cm
3 = 162.999 ℓ
Answer(s): (a) 286.719 ℓ; (b) 162.999 ℓ