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
23 filled with 107256 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 69 cm. Water is then drained from the container and the height of the water level from the base falls to 31 cm.
- What is the capacity of Container G in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container G = 107256 mℓ
13 of Container G = 107256 ÷ 2 = 53628 mℓ
33 of Container G = 53628 x 3 = 160884 mℓ
1 ℓ = 1000 mℓ
Capacity of Container G = 160884 mℓ = 160.884 ℓ
(b)
Fraction of Container G not filled
= 1 -
23 =
13 Height of Container G not filled
=
13 x 69 cm
= 23 cm
Height of Container F
= 69 - 23 - 4
= 42 cm
Volume of remaining water in Container F
= 42 x 42 x 31
= 54684 cm
3 Volume of remaining water in Container G
= 69 x 69 x 31
= 147591 cm
3 Total volume of remaining water in the container
= 54684 + 147591
= 202275 cm
3
1 ℓ = 1000 cm
3 202275 cm
3 = 202.275 ℓ
Answer(s): (a) 160.884 ℓ; (b) 202.275 ℓ