The figure, not drawn to scale, is made of two connected cubical tanks, J and K. Tank J is sealed at the top and completely filled to the brim. Tank K is
23 filled with 105374 mℓ of water. The height of the water level in Tank K is 5 cm higher than that in Tank J. Height of Tank K is 68 cm. Water is then drained from the container and the height of the water level from the base falls to 27 cm.
- What is the capacity of Tank K in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank K = 105374 mℓ
13 of Tank K = 105374 ÷ 2 = 52687 mℓ
33 of Tank K = 52687 x 3 = 158061 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank K = 158061 mℓ = 158.061 ℓ
(b)
Fraction of Tank K not filled
= 1 -
23 =
13 Height of Tank K not filled
=
13 x 68 cm
= 22.666666666667 cm
Height of Tank J
= 68 - 22.666666666667 - 5
= 40.333333333333 cm
Volume of remaining water in Tank J
= 40.333333333333 x 40.333333333333 x 27
= 43922.999999999 cm
3 Volume of remaining water in Tank K
= 68 x 68 x 27
= 124848 cm
3 Total volume of remaining water in the tank
= 43922.999999999 + 124848
= 168771 cm
3
1 ℓ = 1000 cm
3 168771 cm
3 = 168.771 ℓ
Answer(s): (a) 158.061 ℓ; (b) 168.771 ℓ