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 136548 mℓ of water. The height of the water level in Container K is 1 cm higher than that in Container J. Height of Container K is 63 cm. Water is then drained from the container and the height of the water level from the base falls to 28 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 = 136548 mℓ
13 of Container K = 136548 ÷ 2 = 68274 mℓ
33 of Container K = 68274 x 3 = 204822 mℓ
1 ℓ = 1000 mℓ
Capacity of Container K = 204822 mℓ = 204.822 ℓ
(b)
Fraction of Container K not filled
= 1 -
23 =
13 Height of Container K not filled
=
13 x 63 cm
= 21 cm
Height of Container J
= 63 - 21 - 1
= 41 cm
Volume of remaining water in Container J
= 41 x 41 x 28
= 47068 cm
3 Volume of remaining water in Container K
= 63 x 63 x 28
= 111132 cm
3 Total volume of remaining water in the container
= 47068 + 111132
= 158200 cm
3
1 ℓ = 1000 cm
3 158200 cm
3 = 158.2 ℓ
Answer(s): (a) 204.822 ℓ; (b) 158.2 ℓ