Q7 of 32 Page 119

Volume of a cone is 1212 cm3 and its height is 24cm. Find the surface area of the cone.

(π = 22/7)

Given: Volume of cone (V) = 1212 cm3

Height of cone (h) = 24 cm


We know the formula of volume of cone,


Volume = πr2h /3


⇒ 3V = πr2h


⇒ r2 =


⇒


⇒


⇒


⇒ r2 = 48.20 …(i)


⇒ r = √48.20 = 6.94


⇒ r ≈ 7 …(ii)


We know,


l = √(r2 + h2)


⇒ l = √(48.20 + 242) [from (i)]


⇒ l = √(48.20 + 576)


⇒ l = 24.98


⇒ l ≈ 25 …(iii)


⇒ Slant height of cone is 25 cm.


Curved surface area of cone is given by,


CSA = πrl


⇒ [from (ii) and (iii)]


⇒ CSA = 550 …(iv)


Thus, curved surface area of cone is 550 cm2.


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