A cone has a base radius of 6 and a lateral surface area of 12sqrt(34)*pi. Find the volume of the cone.

Answer 1

A_L = π r √(h²+ r²) , r = 6

12π √(34) = 6π√(h²+ 36)

2√(34) = √(h²+ 36)

square the entire equation:

4(34) = h²+36

h² = 100

h = 10

Volume of a cone = (1/3)π r²h = (1/3)π (36)(10) = 120π