The figure, not drawn to scale, is made of two connected cubical containers, Q and R. Container Q is sealed at the top and completely filled to the brim. Container R is
45 filled with 103540 mℓ of water. The height of the water level in Container R is 1 cm higher than that in Container Q. Height of Container R is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 33 cm.
- What is the capacity of Container R in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container R = 103540 mℓ
15 of Container R = 103540 ÷ 4 = 25885 mℓ
55 of Container R = 25885 x 5 = 129425 mℓ
1 ℓ = 1000 mℓ
Capacity of Container R = 129425 mℓ = 129.425 ℓ
(b)
Fraction of Container R not filled
= 1 -
45 =
15 Height of Container R not filled
=
15 x 60 cm
= 12 cm
Height of Container Q
= 60 - 12 - 1
= 47 cm
Volume of remaining water in Container Q
= 47 x 47 x 33
= 72897 cm
3 Volume of remaining water in Container R
= 60 x 60 x 33
= 118800 cm
3 Total volume of remaining water in the container
= 72897 + 118800
= 191697 cm
3
1 ℓ = 1000 cm
3 191697 cm
3 = 191.697 ℓ
Answer(s): (a) 129.425 ℓ; (b) 191.697 ℓ