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
34 filled with 112410 mℓ of water. The height of the water level in Container A is 3 cm higher than that in Container Z. Height of Container A is 56 cm. Water is then drained from the container and the height of the water level from the base falls to 26 cm.
- What is the capacity of Container A in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container A = 112410 mℓ
14 of Container A = 112410 ÷ 3 = 37470 mℓ
44 of Container A = 37470 x 4 = 149880 mℓ
1 ℓ = 1000 mℓ
Capacity of Container A = 149880 mℓ = 149.88 ℓ
(b)
Fraction of Container A not filled
= 1 -
34 =
14 Height of Container A not filled
=
14 x 56 cm
= 14 cm
Height of Container Z
= 56 - 14 - 3
= 39 cm
Volume of remaining water in Container Z
= 39 x 39 x 26
= 39546 cm
3 Volume of remaining water in Container A
= 56 x 56 x 26
= 81536 cm
3 Total volume of remaining water in the container
= 39546 + 81536
= 121082 cm
3
1 ℓ = 1000 cm
3 121082 cm
3 = 121.082 ℓ
Answer(s): (a) 149.88 ℓ; (b) 121.082 ℓ