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 145020 mℓ of water. The height of the water level in Container Q is 1 cm higher than that in Container P. Height of Container Q is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 25 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 = 145020 mℓ
15 of Container Q = 145020 ÷ 3 = 48340 mℓ
55 of Container Q = 48340 x 5 = 241700 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Q = 241700 mℓ = 241.7 ℓ
(b)
Fraction of Container Q not filled
= 1 -
35 =
25 Height of Container Q not filled
=
25 x 65 cm
= 26 cm
Height of Container P
= 65 - 26 - 1
= 38 cm
Volume of remaining water in Container P
= 38 x 38 x 25
= 36100 cm
3 Volume of remaining water in Container Q
= 65 x 65 x 25
= 105625 cm
3 Total volume of remaining water in the container
= 36100 + 105625
= 141725 cm
3
1 ℓ = 1000 cm
3 141725 cm
3 = 141.725 ℓ
Answer(s): (a) 241.7 ℓ; (b) 141.725 ℓ