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 153260 mℓ of water. The height of the water level in Container B is 5 cm higher than that in Container A. Height of Container B is 68 cm. Water is then drained from the container and the height of the water level from the base falls to 36 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 = 153260 mℓ
13 of Container B = 153260 ÷ 2 = 76630 mℓ
33 of Container B = 76630 x 3 = 229890 mℓ
1 ℓ = 1000 mℓ
Capacity of Container B = 229890 mℓ = 229.89 ℓ
(b)
Fraction of Container B not filled
= 1 -
23 =
13 Height of Container B not filled
=
13 x 68 cm
= 22.666666666667 cm
Height of Container A
= 68 - 22.666666666667 - 5
= 40.333333333333 cm
Volume of remaining water in Container A
= 40.333333333333 x 40.333333333333 x 36
= 58563.999999999 cm
3 Volume of remaining water in Container B
= 68 x 68 x 36
= 166464 cm
3 Total volume of remaining water in the container
= 58563.999999999 + 166464
= 225028 cm
3
1 ℓ = 1000 cm
3 225028 cm
3 = 225.028 ℓ
Answer(s): (a) 229.89 ℓ; (b) 225.028 ℓ