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
35 filled with 178845 mℓ of water. The height of the water level in Container S is 5 cm higher than that in Container R. Height of Container S is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 24 cm.
- What is the capacity of Container S in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container S = 178845 mℓ
15 of Container S = 178845 ÷ 3 = 59615 mℓ
55 of Container S = 59615 x 5 = 298075 mℓ
1 ℓ = 1000 mℓ
Capacity of Container S = 298075 mℓ = 298.075 ℓ
(b)
Fraction of Container S not filled
= 1 -
35 =
25 Height of Container S not filled
=
25 x 70 cm
= 28 cm
Height of Container R
= 70 - 28 - 5
= 37 cm
Volume of remaining water in Container R
= 37 x 37 x 24
= 32856 cm
3 Volume of remaining water in Container S
= 70 x 70 x 24
= 117600 cm
3 Total volume of remaining water in the container
= 32856 + 117600
= 150456 cm
3
1 ℓ = 1000 cm
3 150456 cm
3 = 150.456 ℓ
Answer(s): (a) 298.075 ℓ; (b) 150.456 ℓ