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 163668 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 70 cm. Water is then drained from the container and the height of the water level from the base falls to 36 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 = 163668 mℓ
14 of Container L = 163668 ÷ 3 = 54556 mℓ
44 of Container L = 54556 x 4 = 218224 mℓ
1 ℓ = 1000 mℓ
Capacity of Container L = 218224 mℓ = 218.224 ℓ
(b)
Fraction of Container L not filled
= 1 -
34 =
14 Height of Container L not filled
=
14 x 70 cm
= 17.5 cm
Height of Container K
= 70 - 17.5 - 3
= 49.5 cm
Volume of remaining water in Container K
= 49.5 x 49.5 x 36
= 88209 cm
3 Volume of remaining water in Container L
= 70 x 70 x 36
= 176400 cm
3 Total volume of remaining water in the container
= 88209 + 176400
= 264609 cm
3
1 ℓ = 1000 cm
3 264609 cm
3 = 264.609 ℓ
Answer(s): (a) 218.224 ℓ; (b) 264.609 ℓ