The figure, not drawn to scale, is made of two connected cubical containers, J and K. Container J is sealed at the top and completely filled to the brim. Container K is
23 filled with 107806 mℓ of water. The height of the water level in Container K is 3 cm higher than that in Container J. Height of Container K is 57 cm. Water is then drained from the container and the height of the water level from the base falls to 31 cm.
- What is the capacity of Container K in litres?
- What is the volume of water in the container now in litres?
(a)
23 of Container K = 107806 mℓ
13 of Container K = 107806 ÷ 2 = 53903 mℓ
33 of Container K = 53903 x 3 = 161709 mℓ
1 ℓ = 1000 mℓ
Capacity of Container K = 161709 mℓ = 161.709 ℓ
(b)
Fraction of Container K not filled
= 1 -
23 =
13 Height of Container K not filled
=
13 x 57 cm
= 19 cm
Height of Container J
= 57 - 19 - 3
= 35 cm
Volume of remaining water in Container J
= 35 x 35 x 31
= 37975 cm
3 Volume of remaining water in Container K
= 57 x 57 x 31
= 100719 cm
3 Total volume of remaining water in the container
= 37975 + 100719
= 138694 cm
3
1 ℓ = 1000 cm
3 138694 cm
3 = 138.694 ℓ
Answer(s): (a) 161.709 ℓ; (b) 138.694 ℓ