The volume of a hemisphere is numerically equal to three times its curved surface area. Find the radius of the hemisphere.

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1. Volume of a hemisphere is $\frac{2}{3}\pi r^{3}$. Curved surface area is $2\pi r^{2}$.  
2. Given: volume = 3 × curved surface area. So: $\frac{2}{3}\pi r^{3}=3	imes(2\pi r^{2})$.  
3. Cancel $\pi$ and divide by $r^{2}$: $\frac{2}{3}r=6$. So $r=6	imes\frac{3}{2}=9$.  
4. The radius is **9 cm**.

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