The figure, not drawn to scale, is made of two connected cubical containers, B and C. Container B is sealed at the top and completely filled to the brim. Container C is
34 filled with 102060 mℓ of water. The height of the water level in Container C is 4 cm higher than that in Container B. Height of Container C is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 34 cm.
- What is the capacity of Container C in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container C = 102060 mℓ
14 of Container C = 102060 ÷ 3 = 34020 mℓ
44 of Container C = 34020 x 4 = 136080 mℓ
1 ℓ = 1000 mℓ
Capacity of Container C = 136080 mℓ = 136.08 ℓ
(b)
Fraction of Container C not filled
= 1 -
34 =
14 Height of Container C not filled
=
14 x 60 cm
= 15 cm
Height of Container B
= 60 - 15 - 4
= 41 cm
Volume of remaining water in Container B
= 41 x 41 x 34
= 57154 cm
3 Volume of remaining water in Container C
= 60 x 60 x 34
= 122400 cm
3 Total volume of remaining water in the container
= 57154 + 122400
= 179554 cm
3
1 ℓ = 1000 cm
3 179554 cm
3 = 179.554 ℓ
Answer(s): (a) 136.08 ℓ; (b) 179.554 ℓ