Question 508922
slant height is 12 inches and base has a radius of 5 inches.
the surface area of the right circular cone will be pi*5*12 = 60*pi.
here's a nifty little calculator on the web that calculates it for you.
<a href = "http://www.analyzemath.com/Geometry_calculators/surface_volume_cone.html" target = "_blank">http://www.analyzemath.com/Geometry_calculators/surface_volume_cone.html</a>
you have to input the height though.
the formula is:
surface area of a right circular cone = pi*r*sqrt(r^2+h^2)
r is the radius
h is the height.
sqrt(r^2+h^2) turns out to be the slant height which you already have.
if you want to enter numbers into the calculator, you have to find the height.
the pythagorean formula does that.
a^2 + b^2 = c^2
a and b are legs.
c is the hypotenuse.
in your right circular cone, the radius is a and the height is b and the slant height is c.
your formula of a^2 + b^2 + c^2 becomes:
5^2 + b^2 = 12^2
solving for b gets b = sqrt(12^2 - 5^2) which comes out to be sqrt(119) which comes out to be 10.90871211.
if you are to use this calculator, enter 10.90871211 as the radius.
the calculator will tell you that the answer is 188.49556.
60*pi comes out to be 188.4955592 which rounds to 188.49556.
bottom line is the calculator and the equation i showed you above3 are the same.
the surface area is pi * r * slant height.
the calculator formula of sqrt(r^2 + h^2) is the formula for finding the slant height which you already had.