Question #148929
6. If the lateral area of a right circular cylinder is 90 cm2 and its volume is 225 cm3, find its radius.
1
Expert's answer
2020-12-10T20:23:23-0500

Consider a right circular cylinder with radius of base rr and height hh



The volume of the cylinder is V=πr2h.V=\pi r^2h.

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

Then


VF=πr2h2πrh=r2\dfrac{V}{F}=\dfrac{\pi r^2 h}{2\pi rh}=\dfrac{r}{2}

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

Given F=90 cm2,V=225 cm3.F=90\ cm^2, V=225\ cm^3. Then


r=2(225 cm3)90 cm2=5 cmr=\dfrac{2(225\ cm^3)}{90\ cm^2}=5 \ cm

The radius of the cylindeer is 5 cm.



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