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
45 filled with 133796 mℓ of water. The height of the water level in Container Q is 4 cm higher than that in Container P. Height of Container Q is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 35 cm.
- What is the capacity of Container Q in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container Q = 133796 mℓ
15 of Container Q = 133796 ÷ 4 = 33449 mℓ
55 of Container Q = 33449 x 5 = 167245 mℓ
1 ℓ = 1000 mℓ
Capacity of Container Q = 167245 mℓ = 167.245 ℓ
(b)
Fraction of Container Q not filled
= 1 -
45 =
15 Height of Container Q not filled
=
15 x 60 cm
= 12 cm
Height of Container P
= 60 - 12 - 4
= 44 cm
Volume of remaining water in Container P
= 44 x 44 x 35
= 67760 cm
3 Volume of remaining water in Container Q
= 60 x 60 x 35
= 126000 cm
3 Total volume of remaining water in the container
= 67760 + 126000
= 193760 cm
3
1 ℓ = 1000 cm
3 193760 cm
3 = 193.76 ℓ
Answer(s): (a) 167.245 ℓ; (b) 193.76 ℓ