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# cone

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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?

May 18, 2021

#2
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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?

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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

May 18, 2021
edited by jugoslav  May 18, 2021

#1
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Nothing  shown......   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(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

jugoslav May 18, 2021
edited by jugoslav  May 18, 2021