Question

The difference between the outer and inner curved surface area of a hollow right circular cylinder 14 cm long is 88 $c{m}^2$. If the volume of metal used in making the cylinder is 176 $c{m}^3$,find the outer and inner diameters of the cylinder.

Answer 1

We have to find the inner and the outer radius of a hollow cylinder whose height(h) = 14 cm

So,

Outer curved surface area - Inner curved surface area = 88

$\Rightarrow$2$\pi$ (R-r) = 88

$\Rightarrow$ (R-r) = $\frac{88}{2\times \frac{22}{7}\times 14}$

$\Rightarrow$ (R-r) = 1 --------(i)

Also we have,

Volume of outer part - Volume of inner part = 176

$\Rightarrow$ $\pi$ h $(R^2-r^2)$ = 176

$\Rightarrow$ $\pi$ h (R-r) (R+r) = 176

$\Rightarrow$ $\pi$ h (R+r) = 176

$\Rightarrow$ $\frac{22}{7}$ × 14 (R+r) = 176

$\Rightarrow$ (R+r) = 4 -------(ii)

From eq.(i) and (ii)

R = $\frac{5}{2}$

r = $\frac{3}{2}$