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 129354 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 35 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 = 129354 mℓ
13 of Container Z = 129354 ÷ 2 = 64677 mℓ
33 of Container Z = 64677 x 3 = 194031 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Z = 194031 mℓ = 194.031 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 35
= 58835 cm
3 Volume of remaining water in Container Z
= 69 x 69 x 35
= 166635 cm
3 Total volume of remaining water in the container
= 58835 + 166635
= 225470 cm
3
1 ℓ = 1000 cm
3 225470 cm
3 = 225.47 ℓ
Answer(s): (a) 194.031 ℓ; (b) 225.47 ℓ