Q14 of 79 Page 229

The central angle and radius of a sector of a circular disc are 180° and 21 cm respectively. If the edges of the sector are joined together to make a hollow cone, then find the radius of the cone.

Given : Radius of circular disc = r = 21 cm

Central angle of sector = θ = 180°


To find : Radius of cone = R = ?


Formula : Area of sector =


CSA of cone = rl


Solution : When the edges of the sector are joined to form a cone, the radius of the sector becomes the slant height of the cone.


The area of the sector = CSA of the cone


⇒


21 × 21 = × R × 21


= 21R


⇒ R = = = 10.5 cm


∴ The radius of the hollow cone formed by the sector of the circular disc is 10.5 cm.


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