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
35 filled with 108384 mℓ of water. The height of the water level in Container B is 2 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 38 cm.
- What is the capacity of Container B in litres?
- What is the volume of water in the container now in litres?
(a)
35 of Container B = 108384 mℓ
15 of Container B = 108384 ÷ 3 = 36128 mℓ
55 of Container B = 36128 x 5 = 180640 mℓ
1 ℓ = 1000 mℓ
Capacity of Container B = 180640 mℓ = 180.64 ℓ
(b)
Fraction of Container B not filled
= 1 -
35 =
25 Height of Container B not filled
=
25 x 70 cm
= 28 cm
Height of Container A
= 70 - 28 - 2
= 40 cm
Volume of remaining water in Container A
= 40 x 40 x 38
= 60800 cm
3 Volume of remaining water in Container B
= 70 x 70 x 38
= 186200 cm
3 Total volume of remaining water in the container
= 60800 + 186200
= 247000 cm
3
1 ℓ = 1000 cm
3 247000 cm
3 = 247 ℓ
Answer(s): (a) 180.64 ℓ; (b) 247 ℓ