The perimeter of base of a right circular cone is 132 cm. If the height of the cone is 72 cm, then what is the total surface area (in $$cm^2$$) of the cone?

Let radius of cone = $$r$$ cm and height = $$72$$ cm

Perimeter of base = $$2\pi r$$

=> $$2\times\frac{22}{7}\times r=132$$

=> $$r=132\times\frac{7}{44}$$

= $$r=3\times7=21$$ cm

Now, slant height of cone, $$l=\sqrt{h^2+r^2}$$

=> $$l=\sqrt{(72)^2+(21)^2}$$

=> $$l=\sqrt{5184+441}=\sqrt{5625}$$

=> $$l=75$$ cm

$$\therefore$$ Total surface area of the cone = $$\pi r(l+r)$$

= $$(\frac{22}{7}\times21)(75+21)$$

= $$66\times96=6336$$ $$cm^2$$

=> Ans - (B)