Question

A right circular cylinder just encloses a sphere of radius $ r$ (see fig.). Find (i) surface area of the sphere, (ii) curved surface area of the cylinder, (iii) ratio of the areas obtained in(i), and (ii)

Fig. 13.22

Answer 1

(i) Surface area of a sphere $=4{\mathrm{\pi r}}^2$, where r is the radius of the sphere.

(ii) As the Height of the cylinder, $h=r+r=2r$

And Radius of the cylinder $=r$

CSA of cylinder formula $=2\mathrm{\pi rh}=2\mathrm{\pi r}\left(2\mathrm{r}\right)$ (using the value of $h$)

$=4{\mathrm{\pi r}}^2$

(iii) Ratio between areas $=$$\frac{surfaceareaofthesphere}{CSAofcylinder}$

$=\frac{4r^2}{4r^2}=\frac{1}{1}$

Therefore, the ratio of the areas obtained in (i) and (ii) is $1:1$.