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
34 filled with 103806 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 52 cm. Water is then drained from the container and the height of the water level from the base falls to 37 cm.
- What is the capacity of Container L in litres?
- What is the volume of water in the container now in litres?
(a)
34 of Container L = 103806 mℓ
14 of Container L = 103806 ÷ 3 = 34602 mℓ
44 of Container L = 34602 x 4 = 138408 mℓ
1 ℓ = 1000 mℓ
Capacity of Container L = 138408 mℓ = 138.408 ℓ
(b)
Fraction of Container L not filled
= 1 -
34 =
14 Height of Container L not filled
=
14 x 52 cm
= 13 cm
Height of Container K
= 52 - 13 - 1
= 38 cm
Volume of remaining water in Container K
= 38 x 38 x 37
= 53428 cm
3 Volume of remaining water in Container L
= 52 x 52 x 37
= 100048 cm
3 Total volume of remaining water in the container
= 53428 + 100048
= 153476 cm
3
1 ℓ = 1000 cm
3 153476 cm
3 = 153.476 ℓ
Answer(s): (a) 138.408 ℓ; (b) 153.476 ℓ