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 133689 mℓ of water. The height of the water level in Container L is 4 cm higher than that in Container K. Height of Container L is 67 cm. Water is then drained from the container and the height of the water level from the base falls to 32 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 = 133689 mℓ
14 of Container L = 133689 ÷ 3 = 44563 mℓ
44 of Container L = 44563 x 4 = 178252 mℓ
1 ℓ = 1000 mℓ
Capacity of Container L = 178252 mℓ = 178.252 ℓ
(b)
Fraction of Container L not filled
= 1 -
34 =
14 Height of Container L not filled
=
14 x 67 cm
= 16.75 cm
Height of Container K
= 67 - 16.75 - 4
= 46.25 cm
Volume of remaining water in Container K
= 46.25 x 46.25 x 32
= 68450 cm
3 Volume of remaining water in Container L
= 67 x 67 x 32
= 143648 cm
3 Total volume of remaining water in the container
= 68450 + 143648
= 212098 cm
3
1 ℓ = 1000 cm
3 212098 cm
3 = 212.098 ℓ
Answer(s): (a) 178.252 ℓ; (b) 212.098 ℓ