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
34 filled with 160038 mℓ of water. The height of the water level in Tank N is 3 cm higher than that in Tank M. Height of Tank N is 66 cm. Water is then drained from the container and the height of the water level from the base falls to 28 cm.
- What is the capacity of Tank N in litres?
- What is the volume of water in the tank now in litres?
(a)
34 of Tank N = 160038 mℓ
14 of Tank N = 160038 ÷ 3 = 53346 mℓ
44 of Tank N = 53346 x 4 = 213384 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank N = 213384 mℓ = 213.384 ℓ
(b)
Fraction of Tank N not filled
= 1 -
34 =
14 Height of Tank N not filled
=
14 x 66 cm
= 16.5 cm
Height of Tank M
= 66 - 16.5 - 3
= 46.5 cm
Volume of remaining water in Tank M
= 46.5 x 46.5 x 28
= 60543 cm
3 Volume of remaining water in Tank N
= 66 x 66 x 28
= 121968 cm
3 Total volume of remaining water in the tank
= 60543 + 121968
= 182511 cm
3
1 ℓ = 1000 cm
3 182511 cm
3 = 182.511 ℓ
Answer(s): (a) 213.384 ℓ; (b) 182.511 ℓ