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
23 filled with 121954 mℓ of water. The height of the water level in Container L is 2 cm higher than that in Container K. Height of Container L is 60 cm. Water is then drained from the container and the height of the water level from the base falls to 28 cm.
- What is the capacity of Container L in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container L = 121954 mℓ
13 of Container L = 121954 ÷ 2 = 60977 mℓ
33 of Container L = 60977 x 3 = 182931 mℓ
1 ℓ = 1000 mℓ
Capacity of Container L = 182931 mℓ = 182.931 ℓ
(b)
Fraction of Container L not filled
= 1 -
23 =
13 Height of Container L not filled
=
13 x 60 cm
= 20 cm
Height of Container K
= 60 - 20 - 2
= 38 cm
Volume of remaining water in Container K
= 38 x 38 x 28
= 40432 cm
3 Volume of remaining water in Container L
= 60 x 60 x 28
= 100800 cm
3 Total volume of remaining water in the container
= 40432 + 100800
= 141232 cm
3
1 ℓ = 1000 cm
3 141232 cm
3 = 141.232 ℓ
Answer(s): (a) 182.931 ℓ; (b) 141.232 ℓ