Question 113

The volume of a solid right circular cone is $$600 \pi cm^3$$, and the diameter of its base is 30 cm. The total surface area (in cm$$^2$$) of the cone is:

Solution

Let height of cone = $$h$$ cm and radius of base = 15 cm

=> Volume of cone = $$\frac{1}{3}\pi r^2h=600\pi$$

=> $$\frac{1}{3}\times225h=600$$

=> $$h=\frac{600}{75}=8$$ cm

Slant height of cone = $$l=\sqrt{(15)^2+(8)^2}=\sqrt{225+64}$$

=> $$l=\sqrt{289}=17$$ cm

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

= $$15\pi\times(17+15)=480\pi$$ $$cm^2$$

=> Ans - (B)

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