Question

The diameter of the base of a right cone is 12 cm the total surface area of a cone is 306 pi cm^2 what is the length of the slant height

Answer 1

We know that
surface area of the cone (SA)=pi*r²+pi*r*l
where 
r is the radius
l is the slant height
SA=306*pi cm²
diameter=12 cm
r=12/2----> r=6 cm
SA=pi*r²+pi*r*l--------> [SA-pi*r²]=pi*r*l----> l=[SA-pi*r²]/[pi*r]
l=[306*pi-pi*6²]/[pi*6]---> [306*pi-36*pi]/[6*pi]---> 45 cm

the answer is
the length of the slant height is 45 cm