Question 1180609


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*3^2 + pi*3*l}}}
{{{SA = 9pi + 3pi*l}}}...........eq.1

surface area of a hemisphere  SA = 3pi*r^2 

given: {{{r=3}}}

 {{{SA = 3pi*3^2}}} 
{{{SA = 27pi}}}..........eq.2

from eq.1 and eq.2 we have

{{{9pi + 3pi*l=27pi}}}...divide by {{{3}}}

{{{3pi + pi*l=9pi}}}

{{{l=9pi-3pi}}}

{{{l=6pi/ pi}}}

{{{l=6}}}-> slant height

the height of the cone will be

{{{h=sqrt(6^2-3^2)}}}

{{{h=sqrt(36-9)}}}

{{{h=sqrt(25)}}}

{{{h=5}}}


 the height of the cone is {{{5in}}}