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 163576 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 59 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 = 163576 mℓ
15 of Container A = 163576 ÷ 4 = 40894 mℓ
55 of Container A = 40894 x 5 = 204470 mℓ
1 ℓ = 1000 mℓ
Capacity of Container A = 204470 mℓ = 204.47 ℓ
(b)
Fraction of Container A not filled
= 1 -
45 =
15 Height of Container A not filled
=
15 x 59 cm
= 11.8 cm
Height of Container Z
= 59 - 11.8 - 5
= 42.2 cm
Volume of remaining water in Container Z
= 42.2 x 42.2 x 25
= 44521 cm
3 Volume of remaining water in Container A
= 59 x 59 x 25
= 87025 cm
3 Total volume of remaining water in the container
= 44521 + 87025
= 131546 cm
3
1 ℓ = 1000 cm
3 131546 cm
3 = 131.546 ℓ
Answer(s): (a) 204.47 ℓ; (b) 131.546 ℓ