The figure, not drawn to scale, is made of two connected cubical containers, A and B. Container A is sealed at the top and completely filled to the brim. Container B is
23 filled with 120978 mℓ of water. The height of the water level in Container B is 1 cm higher than that in Container A. Height of Container B is 57 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 B in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container B = 120978 mℓ
13 of Container B = 120978 ÷ 2 = 60489 mℓ
33 of Container B = 60489 x 3 = 181467 mℓ
1 ℓ = 1000 mℓ
Capacity of Container B = 181467 mℓ = 181.467 ℓ
(b)
Fraction of Container B not filled
= 1 -
23 =
13 Height of Container B not filled
=
13 x 57 cm
= 19 cm
Height of Container A
= 57 - 19 - 1
= 37 cm
Volume of remaining water in Container A
= 37 x 37 x 37
= 50653 cm
3 Volume of remaining water in Container B
= 57 x 57 x 37
= 120213 cm
3 Total volume of remaining water in the container
= 50653 + 120213
= 170866 cm
3
1 ℓ = 1000 cm
3 170866 cm
3 = 170.866 ℓ
Answer(s): (a) 181.467 ℓ; (b) 170.866 ℓ