The figure, not drawn to scale, is made of two connected cubical containers, G and H. Container G is sealed at the top and completely filled to the brim. Container H is
45 filled with 105172 mℓ of water. The height of the water level in Container H is 1 cm higher than that in Container G. Height of Container H is 70 cm. Water is then drained from the container and the height of the water level from the base falls to 24 cm.
- What is the capacity of Container H in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container H = 105172 mℓ
15 of Container H = 105172 ÷ 4 = 26293 mℓ
55 of Container H = 26293 x 5 = 131465 mℓ
1 ℓ = 1000 mℓ
Capacity of Container H = 131465 mℓ = 131.465 ℓ
(b)
Fraction of Container H not filled
= 1 -
45 =
15 Height of Container H not filled
=
15 x 70 cm
= 14 cm
Height of Container G
= 70 - 14 - 1
= 55 cm
Volume of remaining water in Container G
= 55 x 55 x 24
= 72600 cm
3 Volume of remaining water in Container H
= 70 x 70 x 24
= 117600 cm
3 Total volume of remaining water in the container
= 72600 + 117600
= 190200 cm
3
1 ℓ = 1000 cm
3 190200 cm
3 = 190.2 ℓ
Answer(s): (a) 131.465 ℓ; (b) 190.2 ℓ