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A circle has a radius of 25. A circular sector, with an angle of 345.6 degrees at the center, is cut from the circle, and then rolled to form a cone. Find the volume of the cone.

 

(PS - the answer is not 1344 or 258pi, as I have already tried those answers)

 Oct 29, 2020
 #1
avatar+452 
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A circle has a radius of 25. A circular sector, with an angle of 345.6 degrees at the center, is cut from the circle, and then rolled to form a cone. Find the volume of the cone.

 

r = {[(50 * pi / 360) * 345.6] / pi} / 2

 

r = 24

 

h = sqrt(252 - 242

 

h = 7

 

V = pi*r2*h / 3 = pi*242*7 / 3 = 4222.3 u³   or   1344pi u³

 Oct 29, 2020
edited by Guest  Oct 29, 2020
 #2
avatar+10583 
+1

A circle has a radius of 25. A circular sector, with an angle of 345.6 degrees at the center, is cut from the circle, and then rolled to form a cone. Find the volume of the cone.

 

Hello Guest!

 

\(C_{cone}=2\cdot 25\cdot \pi \cdot \frac{345.6}{360}=\color{blue}150.796\)

\(r_{cone}=\frac{C_{cone}}{2\cdot \pi}=\color{blue}24\)

\(h_{cone}=\sqrt{r_{circle}^2-r_{cone}^2}=\sqrt{25^2-24^2}=\color{blue}7\)

\(V=\frac{1}{3}\cdot \pi \cdot r_{cone}^2\cdot h_{cone}=\frac{1}{3}\cdot \pi \cdot 24^2\cdot 7\)

\(V=4222.3\)

laugh  !

Sorry jugoslav, there was no answer when I started.

 Oct 29, 2020
edited by asinus  Oct 29, 2020
 #3
avatar+452 
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No problem; I appreciate your answers.smiley

jugoslav  Oct 29, 2020

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