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
23 filled with 120570 mℓ of water. The height of the water level in Container A is 4 cm higher than that in Container Z. Height of Container A is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 37 cm.
- What is the capacity of Container A in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container A = 120570 mℓ
13 of Container A = 120570 ÷ 2 = 60285 mℓ
33 of Container A = 60285 x 3 = 180855 mℓ
1 ℓ = 1000 mℓ
Capacity of Container A = 180855 mℓ = 180.855 ℓ
(b)
Fraction of Container A not filled
= 1 -
23 =
13 Height of Container A not filled
=
13 x 69 cm
= 23 cm
Height of Container Z
= 69 - 23 - 4
= 42 cm
Volume of remaining water in Container Z
= 42 x 42 x 37
= 65268 cm
3 Volume of remaining water in Container A
= 69 x 69 x 37
= 176157 cm
3 Total volume of remaining water in the container
= 65268 + 176157
= 241425 cm
3
1 ℓ = 1000 cm
3 241425 cm
3 = 241.425 ℓ
Answer(s): (a) 180.855 ℓ; (b) 241.425 ℓ