What is the lateral area of a cylinder if the height ##h## is ##9## centimeters and the volume ##V## is ##36pi## cubic centimeters?

Lateral area is ##72pi## square centimeters.

As volume is ##pir^2h##, where ##r## is radius and ##h## is height,

##36pi=pir^2xx9## or ##36pi=9pir^2##

Hence ##r^2=(36pi)/(9pi)=4## or ##r=2##

Now lateral area is area of the curved surface of cylinder i.e. ##2pirh##

Hence, lateral area is ##2pixx4xx9=72pi## square centimeters.