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 187539 mℓ of water. The height of the water level in Container G is 3 cm higher than that in Container F. Height of Container G is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 32 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 = 187539 mℓ
14 of Container G = 187539 ÷ 3 = 62513 mℓ
44 of Container G = 62513 x 4 = 250052 mℓ
1 ℓ = 1000 mℓ
Capacity of Container G = 250052 mℓ = 250.052 ℓ
(b)
Fraction of Container G not filled
= 1 -
34 =
14 Height of Container G not filled
=
14 x 70 cm
= 17.5 cm
Height of Container F
= 70 - 17.5 - 3
= 49.5 cm
Volume of remaining water in Container F
= 49.5 x 49.5 x 32
= 78408 cm
3 Volume of remaining water in Container G
= 70 x 70 x 32
= 156800 cm
3 Total volume of remaining water in the container
= 78408 + 156800
= 235208 cm
3
1 ℓ = 1000 cm
3 235208 cm
3 = 235.208 ℓ
Answer(s): (a) 250.052 ℓ; (b) 235.208 ℓ