The figure, not drawn to scale, is made of two connected cubical tanks, M and N. Tank M is sealed at the top and completely filled to the brim. Tank N is
45 filled with 138496 mℓ of water. The height of the water level in Tank N is 4 cm higher than that in Tank M. Height of Tank N is 67 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 N in litres?
- What is the volume of water in the tank now in litres?
(a)
45 of Tank N = 138496 mℓ
15 of Tank N = 138496 ÷ 4 = 34624 mℓ
55 of Tank N = 34624 x 5 = 173120 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank N = 173120 mℓ = 173.12 ℓ
(b)
Fraction of Tank N not filled
= 1 -
45 =
15 Height of Tank N not filled
=
15 x 67 cm
= 13.4 cm
Height of Tank M
= 67 - 13.4 - 4
= 49.6 cm
Volume of remaining water in Tank M
= 49.6 x 49.6 x 25
= 61504 cm
3 Volume of remaining water in Tank N
= 67 x 67 x 25
= 112225 cm
3 Total volume of remaining water in the tank
= 61504 + 112225
= 173729 cm
3
1 ℓ = 1000 cm
3 173729 cm
3 = 173.729 ℓ
Answer(s): (a) 173.12 ℓ; (b) 173.729 ℓ