SOLUTION: A cone and a hemisphere of equal surface area each have a 3-inch radius. What is the height Of the cone?

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Question 1180609: A cone and a hemisphere of equal surface area each
have a 3-inch radius. What is the height Of the
cone?

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

and a hemisphere of equal surface area each have a 3-inch radius. what is the height of the cone?
SA = pi*r^2 + pi*rl
Where,
r is the radius
h is the height
l is the slant height
given: r=3
SA+=+pi%2A3%5E2+%2B+pi%2A3%2Al
SA+=+9pi+%2B+3pi%2Al...........eq.1
surface area of a hemisphere SA = 3pi*r^2
given: r=3
SA+=+3pi%2A3%5E2
SA+=+27pi..........eq.2
from eq.1 and eq.2 we have
9pi+%2B+3pi%2Al=27pi...divide by 3
3pi+%2B+pi%2Al=9pi
l=9pi-3pi
l=6pi%2F+pi
l=6-> slant height
the height of the cone will be
h=sqrt%286%5E2-3%5E2%29
h=sqrt%2836-9%29
h=sqrt%2825%29
h=5

the height of the cone is 5in