A hollow sphere has a volume of k cm\(^3\) and a surface area of k cm\(^2\). Calculate the diameter of the sphere.
Volume of sphere = \(\frac{4}{3}\)πr\(^3\)
Surface area of sphere = 4πr\(^2\)
Since volume and area = k cm\(^3\) and k cm\(^2\)
\(\frac{4}{3}\)πr\(^3\) = 4πr\(^2\)
\(\frac{4}{3}\)r\(^3\) = 4r\(^2\)
4πr\(^3\) = 12πr\(^2\)
r\(^3\) - 3r\(^2\) = 0
r\(^2\)(r - 3) = 0 ⇒ r = 3 cm
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