Answer to Question #145665 in Geometry for Wendy

Question

Find the volume of a right circular cone obtained from a sector of a circle in which the radius is 26 cm and the central angle is 138.5° ?

Answer 1

The circumference of the sector = Length of Arc

Length of Arc = (thetha/360) * 2πr

=(138.5/360) * 2 * (22/7) * 26

= 62.87cm

When the sector is folded, the radius turns to the slant height, l.

Therefore, circumference of circular bottom of cone = 62.87

62.87 = 2πr

r = 62.87 / (2 * (22/7))

r = 10cm

Using Pythagoras' theorem,

l² = r² + h²

h² = l² - r²

h² = 26² - 10²

h =$\sqrt{576}$

h = 24cm.

Volume of cone = (1/3) * B *h

where B = area of circle

= (1/3) * π * r² * h

= (1/3) * (22/7) * 10² * 24

Therefore, volume = 2514.29cm³