Question

The sum of the inner and the outer curved surfaces of a hollow metallic cylinder is $1056$ $c{m}^2$ and the volume of material in it is $1056$ $c{m}^3.$Find the sum of its internal and external radii. Given that the height of the cylinder is $21cm$.

Answer 1

Let us take external radii $=R$

Inner radii=r and height $=21$ cm

As sum of the inner and the outer curved surfaces of a hollow metallic cylinder is $1056$ cm2,

$\pi Rh+\pi rh=1056$

$R+r=8$ ---eq 1

and volume of material $=1056$ $c{m}^3$

$\pi R^{2}h-\pi r^{2}h=1056$

$R^2-r^2=16$

$(R+r)(R-r)=16$

$R-r=2$ ----eq2

After adding eq1 and eq2 we get,

$2R=10$

$R=5$

$r=3$

external radius $R$ is $5$ cm and internal radius $r$ is $3$ cm.

Thus the sum of the external and internal radii is $5+3=8$ cm