A sector with central angle is cut from a circle

Asked by admin @ 03/08/2021 in Math viewed by 308 People

A sector of central angle 216 degree is cut from a circle of radius 25 cm and is rolled up into a cone. What are the base radius and height of the cone ? What is its volume

Answered by admin @ 03/08/2021

Step-by-step explanation:

Radius of the circle = R = 25 cm.

angle of the sector = Ф = 216°.

Length of the circular arc cut off from the circle

= 2 π R * Ф/360°

= 2 * 22/7 * 25 * 216/360 cm

= 94.29 cm

The piece is bent into a right circular cone.

So the slanting height s of the cone = radius of circle = R = 25 cm.

s = 25 cm

circumference of the base of the cone = arc length = 94.29 cm

base radius r of the cone = r = 94.29 * 1/2π = 148.17 cm

height of the cone = h = √(s² - r²) = 25² - 148.17²) = -21329.35 cm

Volume of the cone = V = π/3 * r² h

V = 22/7 * 1/3 * 148.17² * -21329.35 cm³

= −1.046355326×10¹³ cm³

hope it helps mark as brilliant.

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