Question 138

The curved surface area of a right circular cone is 156 $$\pi$$ and the radius of its base is 12 cm. What is the volume of the cone, in cm$$^3$$ ?

Solution

Given that curved surface = 156 $$\pi$$, radius r= 12

$$\Rightarrow \pi r l = 156 \pi $$ (used formula of curved surface )

$$\Rightarrow \pi 12 l = 156 \pi $$ ( radius r= 12 cm)

$$\Rightarrow l = 13 $$

Volume = $$ \dfrac{1}{3} \pi r^2 h $$

$$ \Rightarrow \dfrac{1}{3} \pi 5 \times 144$$ ( h = $$\sqrt{169-144} = \sqrt {25}= 5$$)

$$\Rightarrow 240 \pi $$ Ans

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