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?

Guest May 18, 2021

#2**+2 **

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(r^{2}pi*h)

Cone height h = 4

Cone slant height s = sqrt(r^{2} + h^{2}) = 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**

jugoslav May 18, 2021

#2**+2 **

Best Answer

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(r^{2}pi*h)

Cone height h = 4

Cone slant height s = sqrt(r^{2} + h^{2}) = 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**

jugoslav May 18, 2021