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
23 filled with 153106 mℓ of water. The height of the water level in Container R is 4 cm higher than that in Container Q. Height of Container R is 63 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)
23 of Container R = 153106 mℓ
13 of Container R = 153106 ÷ 2 = 76553 mℓ
33 of Container R = 76553 x 3 = 229659 mℓ
1 ℓ = 1000 mℓ
Capacity of Container R = 229659 mℓ = 229.659 ℓ
(b)
Fraction of Container R not filled
= 1 -
23 =
13 Height of Container R not filled
=
13 x 63 cm
= 21 cm
Height of Container Q
= 63 - 21 - 4
= 38 cm
Volume of remaining water in Container Q
= 38 x 38 x 33
= 47652 cm
3 Volume of remaining water in Container R
= 63 x 63 x 33
= 130977 cm
3 Total volume of remaining water in the container
= 47652 + 130977
= 178629 cm
3
1 ℓ = 1000 cm
3 178629 cm
3 = 178.629 ℓ
Answer(s): (a) 229.659 ℓ; (b) 178.629 ℓ