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 113574 mℓ of water. The height of the water level in Container R is 3 cm higher than that in Container Q. Height of Container R is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 30 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 = 113574 mℓ
13 of Container R = 113574 ÷ 2 = 56787 mℓ
33 of Container R = 56787 x 3 = 170361 mℓ
1 ℓ = 1000 mℓ
Capacity of Container R = 170361 mℓ = 170.361 ℓ
(b)
Fraction of Container R not filled
= 1 -
23 =
13 Height of Container R not filled
=
13 x 66 cm
= 22 cm
Height of Container Q
= 66 - 22 - 3
= 41 cm
Volume of remaining water in Container Q
= 41 x 41 x 30
= 50430 cm
3 Volume of remaining water in Container R
= 66 x 66 x 30
= 130680 cm
3 Total volume of remaining water in the container
= 50430 + 130680
= 181110 cm
3
1 ℓ = 1000 cm
3 181110 cm
3 = 181.11 ℓ
Answer(s): (a) 170.361 ℓ; (b) 181.11 ℓ