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 105718 mℓ of water. The height of the water level in Container L is 3 cm higher than that in Container K. Height of Container L is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 23 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 = 105718 mℓ
13 of Container L = 105718 ÷ 2 = 52859 mℓ
33 of Container L = 52859 x 3 = 158577 mℓ
1 ℓ = 1000 mℓ
Capacity of Container L = 158577 mℓ = 158.577 ℓ
(b)
Fraction of Container L not filled
= 1 -
23 =
13 Height of Container L not filled
=
13 x 63 cm
= 21 cm
Height of Container K
= 63 - 21 - 3
= 39 cm
Volume of remaining water in Container K
= 39 x 39 x 23
= 34983 cm
3 Volume of remaining water in Container L
= 63 x 63 x 23
= 91287 cm
3 Total volume of remaining water in the container
= 34983 + 91287
= 126270 cm
3
1 ℓ = 1000 cm
3 126270 cm
3 = 126.27 ℓ
Answer(s): (a) 158.577 ℓ; (b) 126.27 ℓ