Answer to Question #148929 in Geometry for solid mensuration

Question

6. If the lateral area of a right circular cylinder is 90 cm2 and its volume is 225 cm3, find its radius.

Answer 1

Consider a right circular cylinder with radius of base $r$ and height $h$

The volume of the cylinder is $V=\pi r^2h.$

The lateral area of the cylinder is $F=2\pi rh$

Then

$$\dfrac{V}{F}=\dfrac{\pi r^2 h}{2\pi rh}=\dfrac{r}{2}$$

$$r=\dfrac{2V}{F}$$

Given $F=90\ cm^2, V=225\ cm^3.$ Then

$$r=\dfrac{2(225\ cm^3)}{90\ cm^2}=5 \ cm$$

The radius of the cylindeer is 5 cm.