Question

The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume of the metal used in making the cylinder is 176 cm³, find the outer and inner radii of the cylinder.

Answer 1

Let r and R be the radii of inner and outer surface of a cylinder.

Given, height of cylinder (h) = 14 cm

Volume of cylinder (V) = 176 cm³

and R − r = 1 cm      ...(i)

∵ V = 176 cm²

π (R² − r²) h = 176

`22/7 (R^2 - r^2) xx 14 = 176`

`R^2 - r^2 = (176 xx 7)/(22 xx 14) = 4`

⇒ (R − r) (R + r) = 4

⇒ 1(R + r) = 4

⇒ R + r = 4      ...(ii)

On solving eq. (i) and (ii), we get

2R = 5

R = `5/2` cm

= 2.5 cm

From (i), r = R − 1

`r = 5/2 - 1 = 3/2 = 1.5` cm