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 122874 mℓ of water. The height of the water level in Container B is 4 cm higher than that in Container A. Height of Container B is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 35 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 = 122874 mℓ
13 of Container B = 122874 ÷ 2 = 61437 mℓ
33 of Container B = 61437 x 3 = 184311 mℓ
1 ℓ = 1000 mℓ
Capacity of Container B = 184311 mℓ = 184.311 ℓ
(b)
Fraction of Container B not filled
= 1 -
23 =
13 Height of Container B not filled
=
13 x 63 cm
= 21 cm
Height of Container A
= 63 - 21 - 4
= 38 cm
Volume of remaining water in Container A
= 38 x 38 x 35
= 50540 cm
3 Volume of remaining water in Container B
= 63 x 63 x 35
= 138915 cm
3 Total volume of remaining water in the container
= 50540 + 138915
= 189455 cm
3
1 ℓ = 1000 cm
3 189455 cm
3 = 189.455 ℓ
Answer(s): (a) 184.311 ℓ; (b) 189.455 ℓ