Struggling with this question on finding the surface area of hemisphere. The volume of the hemisphere is 250/3 π. Work out the exact total surface area of the solid hemisphere. Give the answer as a multiple of π?

I got ##75pi##

The area of a sphere is ##4pir^2## so half of it is ##4/2pir^2=2pir^2## and we need to evaluate the radius ##r##;

The volume of the entire sphere is ##V=4/3pir^3##. In your case the volume of the hemisphere should be half or: ##V/2=2/3pir^3## where the volume of the hemisphere is given as ##250/3pi## (I am not sure if it is divided or multiplied by ##pi## so I used multiplied) so we get:

##250/cancel(3)cancel(pi)=2/cancel(3)cancel(pi)r^3##

##r^3=250/2## so that ##r=root(3)(250/2)=5## We can use this value into the expression for half the surface of the sphere BUT....do we need also to consider the base of the hemisphere?

Considering the base as well we get:

##S=2pir^2+pir^2=3pir^2=3pi(5^2)=75pi##