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 118138 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 57 cm. Water is then drained from the container and the height of the water level from the base falls to 20 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 = 118138 mℓ
13 of Container B = 118138 ÷ 2 = 59069 mℓ
33 of Container B = 59069 x 3 = 177207 mℓ
1 ℓ = 1000 mℓ
Capacity of Container B = 177207 mℓ = 177.207 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 - 4
= 34 cm
Volume of remaining water in Container A
= 34 x 34 x 20
= 23120 cm
3 Volume of remaining water in Container B
= 57 x 57 x 20
= 64980 cm
3 Total volume of remaining water in the container
= 23120 + 64980
= 88100 cm
3
1 ℓ = 1000 cm
3 88100 cm
3 = 88.1 ℓ
Answer(s): (a) 177.207 ℓ; (b) 88.1 ℓ