How to find the surface area and the total surface area of a frustum of a cone?

Question

can sum1 plz help me by telling me how i can find the surface area and the total surface area of a frustum of a cone, if you post a equation for it. can you please tell me where the equation comes from or how i use that equation, like do i have to open the shape up.
plz help!!

Answer 1

The lateral surface area of a right circular cone is
S = πrs
where r is the radius of the base and s is the slant height, s = √(r^2 + h^2), with h being the height of the cone.
Let R = the radius of the base of the fustrum,
r = the radius of the top of the fustrum, and
h = the height of the fustrum.
There is some value x which is the height of the missing part of a full cone of radius R so that
x/r = (x + h)/R
xR = xr + hr
x(R - r) = hr
x = hr/(R - r)
The lateral area of the fustrum is the area of the full cone minus the area of the missing top:
S = πR√(R^2 + (h + hr/(R - r))^2) - πr√(r^2 + (hr/(R - r))^2)
S = πR√(R^2 + ((h(R - r) + hr) / (R - r))^2) - πr√(r^2 + (hr/(R - r))^2)
S = πR√(R^2 + (h^2R^2 / (R - r)^2) - πr√(r^2 + (h^2r^2 / (R - r))^2)
S = (π / (R - r)^2)(R√(R^2(R - r)^2 + h^2R^2) - r√(r^2(R - r)^2 + h^2r^2))
S = (π / (R - r)^2)(R^2√((R - r)^2 + h^2) - r^2√((R - r)^2 + h^2))
S = (π / (R - r)^2)(R^2 - r^2)√((R - r)^2 + h^2)

S = (π(R + r) / (R - r))√((R - r)^2 + h^2)

The top and bottom areas total
π(R^2 + r^2)

Answer 2

i can't be of help as far as the frustum, but i can help you out with just the surface area of a cone.

http://en.wikipedia.org/wiki/Cone_%28geometry%29

(Pi)(R) squared + 2(Pi)(R)(L) (L being the slant height. i would say S, but i learned L in Geometry class this year.)

the equation i put down is a little bit different from the one on wikipedia, but it adds up to be the same exact thing. i made it a little bit more understandable so you don't have to bother with the square root of 'r' squared + 'h' squared, which is the slant height. i just put L there and added a 2 to the equation. ingenius, huh? =)

Answer 3

Find the dia. of the base of the cone Pi R squared multiply your answer by the height of the cone and divide the answer by two.

Answer 4

http://en.wikipedia.org/wiki/Frustum

Answer 5

there are of course standard formulae for this, as pointed out by other respondents. however, if i were you i should buy a good book on integral calculus, then you can derive it when needed.

try teach yourself calculus by ABOTT