The figure, not drawn to scale, is made of two connected cubical containers, R and S. Container R is sealed at the top and completely filled to the brim. Container S is
34 filled with 130218 mℓ of water. The height of the water level in Container S is 4 cm higher than that in Container R. Height of Container S is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 23 cm.
- What is the capacity of Container S in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container S = 130218 mℓ
14 of Container S = 130218 ÷ 3 = 43406 mℓ
44 of Container S = 43406 x 4 = 173624 mℓ
1 ℓ = 1000 mℓ
Capacity of Container S = 173624 mℓ = 173.624 ℓ
(b)
Fraction of Container S not filled
= 1 -
34 =
14 Height of Container S not filled
=
14 x 60 cm
= 15 cm
Height of Container R
= 60 - 15 - 4
= 41 cm
Volume of remaining water in Container R
= 41 x 41 x 23
= 38663 cm
3 Volume of remaining water in Container S
= 60 x 60 x 23
= 82800 cm
3 Total volume of remaining water in the container
= 38663 + 82800
= 121463 cm
3
1 ℓ = 1000 cm
3 121463 cm
3 = 121.463 ℓ
Answer(s): (a) 173.624 ℓ; (b) 121.463 ℓ