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 194580 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 69 cm. Water is then drained from the container and the height of the water level from the base falls to 32 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 = 194580 mℓ
14 of Tank N = 194580 ÷ 3 = 64860 mℓ
44 of Tank N = 64860 x 4 = 259440 mℓ
1 ℓ = 1000 mℓ
Capacity of Tank N = 259440 mℓ = 259.44 ℓ
(b)
Fraction of Tank N not filled
= 1 -
34 =
14 Height of Tank N not filled
=
14 x 69 cm
= 17.25 cm
Height of Tank M
= 69 - 17.25 - 4
= 47.75 cm
Volume of remaining water in Tank M
= 47.75 x 47.75 x 32
= 72962 cm
3 Volume of remaining water in Tank N
= 69 x 69 x 32
= 152352 cm
3 Total volume of remaining water in the tank
= 72962 + 152352
= 225314 cm
3
1 ℓ = 1000 cm
3 225314 cm
3 = 225.314 ℓ
Answer(s): (a) 259.44 ℓ; (b) 225.314 ℓ