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
25 filled with 111852 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 70 cm. Water is then drained from the container and the height of the water level from the base falls to 31 cm.
- What is the capacity of Container B in litres?
- What is the volume of water in the container now in litres?
(a)
25 of Container B = 111852 mℓ
15 of Container B = 111852 ÷ 2 = 55926 mℓ
55 of Container B = 55926 x 5 = 279630 mℓ
1 ℓ = 1000 mℓ
Capacity of Container B = 279630 mℓ = 279.63 ℓ
(b)
Fraction of Container B not filled
= 1 -
25 =
35 Height of Container B not filled
=
35 x 70 cm
= 42 cm
Height of Container A
= 70 - 42 - 5
= 23 cm
Volume of remaining water in Container A
= 23 x 23 x 31
= 16399 cm
3 Volume of remaining water in Container B
= 70 x 70 x 31
= 151900 cm
3 Total volume of remaining water in the container
= 16399 + 151900
= 168299 cm
3
1 ℓ = 1000 cm
3 168299 cm
3 = 168.299 ℓ
Answer(s): (a) 279.63 ℓ; (b) 168.299 ℓ