#### Problem Statement: CE Board November 1997

Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and central angle of 210°.

- A. 12367.2 cm
^{3} - B. 13232.6 cm
^{3} - C. 13503.4 cm
^{3} - D. 14682.5 cm
^{3}

#### Problem Answer:

The volume of a cone to be constructed from a sector is **13503.4 cu. cm**.

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What happened to 210°? Where is it?

Isn’t this wrong? Since the arc of the sector should be equal to the circumference of the base of the cone

Since arc length of sector is equal to the circumference of the base of the cone:

C (sub2) = C —-> 1

let X= be the radius of the base of the cone

1 —-> 2piX=36*210*(pi/180)

X=21

from the cone: (pythagorean theorem)

let h: altitude of cone

r: radius of the sector

r^2=X^2 + h^2

(72)^2 = (21)^2 + h^2

h = 3*sqrt of 527

Volume (subCONE) = (1/3) * Area of the base * altitude

= (1/3) * pi* (21)^2 * 3*sqrt of 527

= 31, 805 cm^3