1. Your friend’s cap is in the shape of a right circular cone of base radius 14 cm and height 26.5 cm. The approximate area of the sheet required to make 7 such caps is






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  • By: anil on 05 May 2019 02.39 am
    A cone is formed when the 2 edges of the sector of a circle are joined. 

    We have to find the central angle subtended to find out the area of the sheet required to make the cone. 
    It has been given that the height of the cone is 26.5 cm and the base radius is 14 cm. 

    The slant height of the cone will be equal to the radius of the sector of the circle. 

    Slant height = $$sqrt{26.5^2+14^2}$$ = $$sqrt{898.25}$$
    $$sqrt{898.25}$$ is very close in value to $$sqrt{900}$$

    Let us use $$sqrt{900}$$ for the ease of calculation.
    $$sqrt{900}$$ = $$30$$ cm.
    Therefore, the radius of the sector of the circle is 30 cm. 

    The length of the arc subtended will be equal to the perimeter of the base circle. 
    => Length of the arc subtended = $$2*(22/7)*14$$= $$88$$ cm. 

    Length of arc = $$88$$ cm.
    Perimeter of the entire circle = $$2*frac{22}{7}*30$$ = $$188$$ cm.
    Area of the sector = $$frac{88}{188}*frac{22}{7}*30^2$$
                                = $$frac{9268}{7}$$ $$cm^2$$.

    We have to find the area of sheet required to form 7 such cones. 
    Therefore, total area of sheet required = $$7*frac{9268}{7}$$ = $$9268 cm^2$$

    $$9240$$ is the closest value among the given options. Therefore, option D is the right answer.


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