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)

Guest Oct 29, 2020

#1**+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.

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

r = 24

h = sqrt(25^{2} - 24^{2})

h = 7

V = pi*r^{2}*h / 3 = pi*24^{2}*7 / 3 = 4222.3 u³ or 1344pi u³

jugoslav Oct 29, 2020

edited by
Guest
Oct 29, 2020

#2**+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!**

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

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

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

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

\(V=4222.3\)

!

**Sorry jugoslav**, there was no answer when I started.

asinus Oct 29, 2020