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 114861 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 60 cm. Water is then drained from the container and the height of the water level from the base falls to 22 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 = 114861 mℓ
14 of Container L = 114861 ÷ 3 = 38287 mℓ
44 of Container L = 38287 x 4 = 153148 mℓ
1 ℓ = 1000 mℓ
Capacity of Container L = 153148 mℓ = 153.148 ℓ
(b)
Fraction of Container L not filled
= 1 -
34 =
14 Height of Container L not filled
=
14 x 60 cm
= 15 cm
Height of Container K
= 60 - 15 - 3
= 42 cm
Volume of remaining water in Container K
= 42 x 42 x 22
= 38808 cm
3 Volume of remaining water in Container L
= 60 x 60 x 22
= 79200 cm
3 Total volume of remaining water in the container
= 38808 + 79200
= 118008 cm
3
1 ℓ = 1000 cm
3 118008 cm
3 = 118.008 ℓ
Answer(s): (a) 153.148 ℓ; (b) 118.008 ℓ