The figure, not drawn to scale, is made of two connected cubical containers, P and Q. Container P is sealed at the top and completely filled to the brim. Container Q is
35 filled with 115821 mℓ of water. The height of the water level in Container Q is 3 cm higher than that in Container P. Height of Container Q is 70 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 Q in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container Q = 115821 mℓ
15 of Container Q = 115821 ÷ 3 = 38607 mℓ
55 of Container Q = 38607 x 5 = 193035 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Q = 193035 mℓ = 193.035 ℓ
(b)
Fraction of Container Q not filled
= 1 -
35 =
25 Height of Container Q not filled
=
25 x 70 cm
= 28 cm
Height of Container P
= 70 - 28 - 3
= 39 cm
Volume of remaining water in Container P
= 39 x 39 x 23
= 34983 cm
3 Volume of remaining water in Container Q
= 70 x 70 x 23
= 112700 cm
3 Total volume of remaining water in the container
= 34983 + 112700
= 147683 cm
3
1 ℓ = 1000 cm
3 147683 cm
3 = 147.683 ℓ
Answer(s): (a) 193.035 ℓ; (b) 147.683 ℓ