What is the slant height of a cone with a diameter of 10 in and a surface area of 90π in^2?

Question

What is the slant height of a cone with a diameter of 10 in and a surface area of 90pi in^2 ?

Answer 1

If your surface area of the cone includes the base, the formula is Area = πr(s + r). The πrs part is the curved surface area, the πr² part is the cone's base area.

For this problem 90π = π5(s + 5) where r is the radius of 5 and s is the slant height. The π's cancel out, so you're left with 90 = 5(s + 5). Can you calc "s" from there?

If you don't include the base of the cone, use A = πrs.

Answer 2

Let A =πrl + πr² where l is the slant height hence 90π =π(rl +r²) and 90 = 5l + 25 or 18= l +5 and l= 13in for the slant height.