Q7 of 32 Page 123

Total surface area of a cone is 616 sq.cm. If the slant height of the cone is three times the radius of its base, find its slant height.

Given: Total surface area of cone = 616 cm2

According to the question,


Slant height of cone = 3 (radius of the base of cone)


Let slant height of cone = l


And let radius of the base of cone = r


Then, l = 3r …(i)


Total surface area of cone is given by,


TSA = πrl + πr2


Substituting TSA = 616 cm2,


616 = πr(3r) + πr2 [Using equation (i)]


⇒ 616 = 3πr2 + πr2


⇒ 616 = 4πr2


⇒


⇒


⇒


⇒


⇒ r2 = 49


⇒ r = √49


⇒ r = 7


Putting r = 7 in equation (i), we get


l = 3 × 7 = 21


Thus, slant height of cone is 21 cm.


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