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
45 filled with 171116 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 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)
45 of Tank K = 171116 mℓ
15 of Tank K = 171116 ÷ 4 = 42779 mℓ
55 of Tank K = 42779 x 5 = 213895 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank K = 213895 mℓ = 213.895 ℓ
(b)
Fraction of Tank K not filled
= 1 -
45 =
15 Height of Tank K not filled
=
15 x 69 cm
= 13.8 cm
Height of Tank J
= 69 - 13.8 - 5
= 50.2 cm
Volume of remaining water in Tank J
= 50.2 x 50.2 x 25
= 63001 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
= 63001 + 119025
= 182026 cm
3
1 ℓ = 1000 cm
3 182026 cm
3 = 182.026 ℓ
Answer(s): (a) 213.895 ℓ; (b) 182.026 ℓ