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
35 filled with 168516 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 70 cm. Water is then drained from the container and the height of the water level from the base falls to 31 cm.
- What is the capacity of Container Z in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container Z = 168516 mℓ
15 of Container Z = 168516 ÷ 3 = 56172 mℓ
55 of Container Z = 56172 x 5 = 280860 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Z = 280860 mℓ = 280.86 ℓ
(b)
Fraction of Container Z not filled
= 1 -
35 =
25 Height of Container Z not filled
=
25 x 70 cm
= 28 cm
Height of Container Y
= 70 - 28 - 3
= 39 cm
Volume of remaining water in Container Y
= 39 x 39 x 31
= 47151 cm
3 Volume of remaining water in Container Z
= 70 x 70 x 31
= 151900 cm
3 Total volume of remaining water in the container
= 47151 + 151900
= 199051 cm
3
1 ℓ = 1000 cm
3 199051 cm
3 = 199.051 ℓ
Answer(s): (a) 280.86 ℓ; (b) 199.051 ℓ