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
45 filled with 158508 mℓ of water. The height of the water level in Container S is 1 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 28 cm.
- What is the capacity of Container S in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container S = 158508 mℓ
15 of Container S = 158508 ÷ 4 = 39627 mℓ
55 of Container S = 39627 x 5 = 198135 mℓ
1 ℓ = 1000 mℓ
Capacity of Container S = 198135 mℓ = 198.135 ℓ
(b)
Fraction of Container S not filled
= 1 -
45 =
15 Height of Container S not filled
=
15 x 70 cm
= 14 cm
Height of Container R
= 70 - 14 - 1
= 55 cm
Volume of remaining water in Container R
= 55 x 55 x 28
= 84700 cm
3 Volume of remaining water in Container S
= 70 x 70 x 28
= 137200 cm
3 Total volume of remaining water in the container
= 84700 + 137200
= 221900 cm
3
1 ℓ = 1000 cm
3 221900 cm
3 = 221.9 ℓ
Answer(s): (a) 198.135 ℓ; (b) 221.9 ℓ