A sector of area 427cm2 is cut out of a thin circular sheet of radius 17cm. It is then folded, with straight edges coinciding to form a cone. Calculate: a. The angle of the sector &nbsp; &nbsp; b. The length of the arc of the sector, &nbsp; c. The height of the circular cone.

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A sector of area 427cm2 is cut out of a thin circular sheet of radius 17cm. It is then folded, with straight edges coinciding to form a cone. Calculate: a. The angle of the sector &amp;nbsp; &amp;nbsp; b. The length of the arc of the sector, &amp;nbsp; c. The height of the circular cone.

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(a) Area of sector,&amp;nbsp;A&amp;nbsp;=&amp;nbsp;427cm2&amp;nbsp;, radius of circular metal, R = 7cm, let&amp;nbsp;Ø&amp;nbsp;= angle of sector&amp;nbsp;→A=θ360×πR2→427=θ360×3.142×172→θ=169o(b) Lenght of arc&amp;nbsp;=θ360×2πR=169360×2×3.142×17=50.2cm(c) Circumference of cone = length of arc = 50.2cm&amp;nbsp;→2πr=50.2→r=7.99cmFrom figure of the cone above l = R = 17cm,&amp;nbsp;By Pythagoras theorem,&amp;nbsp;l2&amp;nbsp;=&amp;nbsp;h2&amp;nbsp;+&amp;nbsp;r2&amp;nbsp;implies, h = 15.01cm&amp;nbsp;NB:&amp;nbsp;1. in finding the base radius of a cone, we use the following formula:&amp;nbsp;rR=θ360×R2. Again, we find the semi-vertical angle&amp;nbsp;αby using:&amp;nbsp;sin&amp;nbsp;α=rR

A sector of area 427cm2 is cut out

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