Question

A right cone has a volume 100pie and height of 12. whats the total area?

Answer 1

What's the formula for a cone?

Answer 2

http://www.analyzemath.com/Geometry_calculators/cone_1.gif

Answer 3

Using that, how can we derive the radius?

Answer 4

So, using the two formulas generously donated above.....\[V=100\pi=\frac{\pi r^2(12)}{3}=\implies 5=r \implies A=\pi r \sqrt{5^2+12^2}=65 \pi\]

Answer 5

The volume of the cone is given by the formula V = (1/3) B h where B is the area of the base.
V = (1/3) pi*r^2 * h
100 pi = (1/3) pi * r^2 (12)
100 pi = 4 pi r^2
25 = r^2
5 = r
---------
SA = pi * r * slant height + B
SA = pi * (5) * (13) + pi * 5^2
SA = 65 pi + 25 pi
SA = 90 pi

Answer 6

Nice work. I didn't check the formula very well, I guess.

Answer 7

Just to prove I can do it correctly...\[V=100π=\frac{πr^2(12)}3⟹5=r⟹A=πr (\sqrt{5^2+12^2}+r)=90π\]