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
23 filled with 118766 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 69 cm. Water is then drained from the container and the height of the water level from the base falls to 34 cm.
- What is the capacity of Tank N in litres?
- What is the volume of water in the tank now in litres?
(a)
23 of Tank N = 118766 mℓ
13 of Tank N = 118766 ÷ 2 = 59383 mℓ
33 of Tank N = 59383 x 3 = 178149 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank N = 178149 mℓ = 178.149 ℓ
(b)
Fraction of Tank N not filled
= 1 -
23 =
13 Height of Tank N not filled
=
13 x 69 cm
= 23 cm
Height of Tank M
= 69 - 23 - 3
= 43 cm
Volume of remaining water in Tank M
= 43 x 43 x 34
= 62866 cm
3 Volume of remaining water in Tank N
= 69 x 69 x 34
= 161874 cm
3 Total volume of remaining water in the tank
= 62866 + 161874
= 224740 cm
3
1 ℓ = 1000 cm
3 224740 cm
3 = 224.74 ℓ
Answer(s): (a) 178.149 ℓ; (b) 224.74 ℓ