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 109124 mℓ of water. The height of the water level in Container Z is 5 cm higher than that in Container Y. Height of Container Z is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 36 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 = 109124 mℓ
13 of Container Z = 109124 ÷ 2 = 54562 mℓ
33 of Container Z = 54562 x 3 = 163686 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Z = 163686 mℓ = 163.686 ℓ
(b)
Fraction of Container Z not filled
= 1 -
23 =
13 Height of Container Z not filled
=
13 x 69 cm
= 23 cm
Height of Container Y
= 69 - 23 - 5
= 41 cm
Volume of remaining water in Container Y
= 41 x 41 x 36
= 60516 cm
3 Volume of remaining water in Container Z
= 69 x 69 x 36
= 171396 cm
3 Total volume of remaining water in the container
= 60516 + 171396
= 231912 cm
3
1 ℓ = 1000 cm
3 231912 cm
3 = 231.912 ℓ
Answer(s): (a) 163.686 ℓ; (b) 231.912 ℓ