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 123476 mℓ of water. The height of the water level in Tank N is 5 cm higher than that in Tank M. Height of Tank N is 55 cm. Water is then drained from the container and the height of the water level from the base falls to 33 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 = 123476 mℓ
15 of Tank N = 123476 ÷ 4 = 30869 mℓ
55 of Tank N = 30869 x 5 = 154345 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank N = 154345 mℓ = 154.345 ℓ
(b)
Fraction of Tank N not filled
= 1 -
45 =
15 Height of Tank N not filled
=
15 x 55 cm
= 11 cm
Height of Tank M
= 55 - 11 - 5
= 39 cm
Volume of remaining water in Tank M
= 39 x 39 x 33
= 50193 cm
3 Volume of remaining water in Tank N
= 55 x 55 x 33
= 99825 cm
3 Total volume of remaining water in the tank
= 50193 + 99825
= 150018 cm
3
1 ℓ = 1000 cm
3 150018 cm
3 = 150.018 ℓ
Answer(s): (a) 154.345 ℓ; (b) 150.018 ℓ