When 3 litres of oil is removed from an upright cylindrical can the level falls by 10cm. Find the radius of the can

Question

Should i use: pie r² h ??

Answer 1

1 L = 10^-3 m³

 

The volume of a cylinder is:

V (m³) = π * r² (m²) * h (m)

 

where h is the height of the oil in this problem.

 

When 3 litres (or 3*10^-3  m³) of oil is removed, the level falls by 10 cm, meaning that the new height of the oil is:

 

h' (m) = h (m) - 0.1

 

and the new volume of the oil is:

 

V' (m³) = V - 3*10^-3

            = π * r² * h'

 

So you have:

 

π * r² * h - 0.003 = π * r² * (h-0.1)

π * r² * h - 0.003 = π * r² * h - π * r² * 0.1

- 0.003 =  - π * r² * 0.1

r² = 0.003/(π*0.1)

r = sqrt(0.003/(π*0.1))

r = 0.098 m

r = 9.8 cm