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

Question

anonymous · Answer

What's the formula for a cone?

eyust707 · Answer

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

anonymous · Answer

Using that, how can we derive the radius?

anonymous · Answer

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

directrix · Answer

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

directrix · Answer

attachment

anonymous · Answer

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

anonymous · Answer

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