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 193864 mℓ of water. The height of the water level in Tank K is 1 cm higher than that in Tank J. Height of Tank K is 69 cm. Water is then drained from the container and the height of the water level from the base falls to 25 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 = 193864 mℓ
13 of Tank K = 193864 ÷ 2 = 96932 mℓ
33 of Tank K = 96932 x 3 = 290796 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank K = 290796 mℓ = 290.796 ℓ
(b)
Fraction of Tank K not filled
= 1 -
23 =
13 Height of Tank K not filled
=
13 x 69 cm
= 23 cm
Height of Tank J
= 69 - 23 - 1
= 45 cm
Volume of remaining water in Tank J
= 45 x 45 x 25
= 50625 cm
3 Volume of remaining water in Tank K
= 69 x 69 x 25
= 119025 cm
3 Total volume of remaining water in the tank
= 50625 + 119025
= 169650 cm
3
1 ℓ = 1000 cm
3 169650 cm
3 = 169.65 ℓ
Answer(s): (a) 290.796 ℓ; (b) 169.65 ℓ