The figure, not drawn to scale, is made of two connected cubical containers, Z and A. Container Z is sealed at the top and completely filled to the brim. Container A is
45 filled with 180756 mℓ of water. The height of the water level in Container A is 5 cm higher than that in Container Z. Height of Container A is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 25 cm.
- What is the capacity of Container A in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container A = 180756 mℓ
15 of Container A = 180756 ÷ 4 = 45189 mℓ
55 of Container A = 45189 x 5 = 225945 mℓ
1 ℓ = 1000 mℓ
Capacity of Container A = 225945 mℓ = 225.945 ℓ
(b)
Fraction of Container A not filled
= 1 -
45 =
15 Height of Container A not filled
=
15 x 65 cm
= 13 cm
Height of Container Z
= 65 - 13 - 5
= 47 cm
Volume of remaining water in Container Z
= 47 x 47 x 25
= 55225 cm
3 Volume of remaining water in Container A
= 65 x 65 x 25
= 105625 cm
3 Total volume of remaining water in the container
= 55225 + 105625
= 160850 cm
3
1 ℓ = 1000 cm
3 160850 cm
3 = 160.85 ℓ
Answer(s): (a) 225.945 ℓ; (b) 160.85 ℓ