The radius and height of a cone are in the ratio 4:3 . The area of the base is 154 cm^2 . Find the area of the curved surface .

Answers (1)

Solution:  Let r be the radius and h be the height of the cone . it is given that 

                  fracrh= frac43

          Let r= 4x   and h= 3x

Now , Area of the base = 154  cm^2

Rightarrow                pi r^2=154

Rightarrow                frac227	imes (4x)^2=154

Rightarrow               frac227	imes 16 x^2=154

Rightarrow                           x^2= frac154	imes 722	imes 16=frac4916Rightarrow x= sqrtfrac4916=frac74cm

	herefore                         r=4x=4	imes frac74cm ,       and      h= 3 	imes frac74=frac214cm

Let the slant height be l cm . Then, 

                        l^2=r^2+h^2

Rightarrow                    l=sqrtr^2+h^2=sqrt7^2+ (frac214)^2cm = sqrt49+frac44116=frac354cm

	herefore              curved surface area 

                                              =pi rl = frac227	imes7	imes frac354cm^2=192.5cm^2

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