The figure, not drawn to scale, is made of two connected cubical containers, F and G. Container F is sealed at the top and completely filled to the brim. Container G is
34 filled with 123951 mℓ of water. The height of the water level in Container G is 4 cm higher than that in Container F. Height of Container G is 56 cm. Water is then drained from the container and the height of the water level from the base falls to 37 cm.
- What is the capacity of Container G in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container G = 123951 mℓ
14 of Container G = 123951 ÷ 3 = 41317 mℓ
44 of Container G = 41317 x 4 = 165268 mℓ
1 ℓ = 1000 mℓ
Capacity of Container G = 165268 mℓ = 165.268 ℓ
(b)
Fraction of Container G not filled
= 1 -
34 =
14 Height of Container G not filled
=
14 x 56 cm
= 14 cm
Height of Container F
= 56 - 14 - 4
= 38 cm
Volume of remaining water in Container F
= 38 x 38 x 37
= 53428 cm
3 Volume of remaining water in Container G
= 56 x 56 x 37
= 116032 cm
3 Total volume of remaining water in the container
= 53428 + 116032
= 169460 cm
3
1 ℓ = 1000 cm
3 169460 cm
3 = 169.46 ℓ
Answer(s): (a) 165.268 ℓ; (b) 169.46 ℓ