Question 1196414
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For simplicity I will leave off the units in my discussion.<br>
The circular sector is 5/6 of the whole circle.  The length of the curved part of the sector is 5/6 of the circumference of a circle with radius 6: {{{(5/6)(2pi)(6)=10pi}}}<br>
That curved part of the sector becomes the circumference of the base of the cone.  The radius of the cone is the circumference of its base, divided by 2pi: {{{(10pi)/(2pi)=5}}}<br>
ANSWER a. The radius of the base of the cone is 5<br>
The slant height of the cone is the radius of the sector: 6.<br>
The radius of the base of the cone is 5; the slant height is 6; the Pythagorean Theorem tells us the height of the cone is {{{sqrt(11)}}}.<br>
The volume of the cone is one-third the area of the base, times the height:<br>
{{{V=(1/3)((pi)(5^2))(sqrt(11))}}}<br>
ANSWER b. The volume of the cone is {{{((25/3)sqrt(11))pi}}}<br>