SOLUTION: this question is in my saxon algebra 3 book and i cant figure it out find the surface area of a right circular cone whose slant height is 12 in and whos base has a radius of 5

Question 508922: this question is in my saxon algebra 3 book and i cant figure it out
find the surface area of a right circular cone whose slant height is 12 in and whos base has a radius of 5 in
Found 2 solutions by Theo, Earlsdon:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.
http://www.analyzemath.com/Geometry_calculators/surface_volume_cone.html
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.

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Find the surface area of a right circulr cone:
Note:
The "lateral surface" area (S) of a cone does not include the area of the base.
The "total surface" (T) area of a cone included the area of the base.
Let's do both and you can choose which anwer is appropriate.
1) Lateral surface area (area of base not included) is:
where: r is the radius of the base and s is the slant height.

sq.in. This is the exact answer.
sq.in. This an approximate answer. (I just multiplied by 3.14 for .
2) Total surface area (area of base is included) is:
where: r is the radius of the base and s is the slant height.

sq.in. This is the exact answer.
sq.in. This an approximate answer. (I just multiplied by 3.14).

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