How do you calculate the radius of a hemispherical solid whose total surface area is #48pi# #cm^2#?

1 Answer
Shwetank Mauria
Nov 22, 2016

Radius of hemisphere is #4# #cm.#

Explanation:

Curved surface area of a hemisphere of radius #r# is half of the surface area of a sphere of radius #r#. As latter is #4pir^2#, curved surface area of a hemisphere of radius #r# is #2pir^2#.

Further the flat surface of hemisphere is a circle of radius #r# and its area is #pir^2#

and hence total surface area of hemisphere is #2pir^2+pir^2=3pir^2#.

As this is #48pi# #cm^2#, we have #3pir^2=48pi#

and #r^2=(48pi)/(3pi)=16# and #r=4#

Hence, radius of hemisphere is #4# #cm.#

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