Discussion
The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12cm each. The radius of the sphere is.
Answer: C
The cylinder has diameter 12 cm, so \( r = 6 \) cm, and \( h = 12 \) cm.
\[ \text{CSA of cylinder} = 2\pi r h = 2\pi (6)(12) = 144\pi \text{ cm}^{2} \]
Setting the sphere's surface area equal to it:
\[ 4\pi R^{2} = 144\pi \quad\Longrightarrow\quad R^{2} = 36 \quad\Longrightarrow\quad R = 6 \text{ cm} \]
Using the diameter 12 in place of the radius in the cylinder formula would give \( 288\pi \) and a sphere of radius \( 6\sqrt{2} \) - the reason 12 cm is on the list.
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