Question

MATHEMATICAL CONNECTIONS The value of the surface area of the cylinder is equal to the value of the volume of the cylinder. Find the value of x.
2.5 cm

x cm

Find the surface area and volume of the cylinder.

Surface area =

i cm2

Volume =

it cm

Answer 1

Given :

The value of the surface area of the cylinder is equal to the value of the volume of the cylinder.

To Find :

The relation between height and radius.

Solution :

$S.A=2\pi rh+2\pi r^2=2\pi r(h+r)$

$V=\pi r^2h$

Now ,

$S.A=V\\\\2\pi r(h+r)=\pi r^2h\\\\2(h+r)=rh\\\\2h+2r=rh\\\\h(2-r)=-2r\\\\h=\dfrac{2r}{r-2}$

Hence, this is the required solution.