From a circular piece of paper with radius BC , Jeff removes the unshaded sector shown. Using the larger shaded sector, he joins edge BC to edge BA (without overlap) to form a cone of radius 18 centimeters and of volume 432*pi cubic centimeters. What is the number of degrees in the measure of angle ABC of the sector that is not used?
+1639 From a circular piece of paper with radius BC, Jeff removes the unshaded sector shown. Using the larger shaded sector, he joins edge BC to edge BA (without overlap) to form a cone of radius 18 centimeters and of volume 432*pi cubic centimeters. What is the number of degrees in the measure of angle ABC of the sector that is not used?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Cone radius r = 18
Cone volume V = 432pi
Knowing this, we can calculate the height of a cone:
V = 1/3(r2pi*h)
Cone height h = 4
Cone slant height s = sqrt(r2 + h2) = 2√85
Note that slant height s is also radius BC.
The length of major arc AC is also the length of the circumference of a base of a cone.
So, the bottom line is:
Angle ABC = 8.572658425º
+1639 From a circular piece of paper with radius BC, Jeff removes the unshaded sector shown. Using the larger shaded sector, he joins edge BC to edge BA (without overlap) to form a cone of radius 18 centimeters and of volume 432*pi cubic centimeters. What is the number of degrees in the measure of angle ABC of the sector that is not used?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Cone radius r = 18
Cone volume V = 432pi
Knowing this, we can calculate the height of a cone:
V = 1/3(r2pi*h)
Cone height h = 4
Cone slant height s = sqrt(r2 + h2) = 2√85
Note that slant height s is also radius BC.
The length of major arc AC is also the length of the circumference of a base of a cone.
So, the bottom line is:
Angle ABC = 8.572658425º
