The figure, not drawn to scale, is made of two connected cubical containers, K and L. Container K is sealed at the top and completely filled to the brim. Container L is
45 filled with 184352 mℓ of water. The height of the water level in Container L is 1 cm higher than that in Container K. Height of Container L is 65 cm. Water is then drained from the container and the height of the water level from the base falls to 35 cm.
- What is the capacity of Container L in litres?
- What is the volume of water in the container now in litres?
(a)
45 of Container L = 184352 mℓ
15 of Container L = 184352 ÷ 4 = 46088 mℓ
55 of Container L = 46088 x 5 = 230440 mℓ
1 ℓ = 1000 mℓ
Capacity of Container L = 230440 mℓ = 230.44 ℓ
(b)
Fraction of Container L not filled
= 1 -
45 =
15 Height of Container L not filled
=
15 x 65 cm
= 13 cm
Height of Container K
= 65 - 13 - 1
= 51 cm
Volume of remaining water in Container K
= 51 x 51 x 35
= 91035 cm
3 Volume of remaining water in Container L
= 65 x 65 x 35
= 147875 cm
3 Total volume of remaining water in the container
= 91035 + 147875
= 238910 cm
3
1 ℓ = 1000 cm
3 238910 cm
3 = 238.91 ℓ
Answer(s): (a) 230.44 ℓ; (b) 238.91 ℓ