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Mathematics

If the number of square centimeters on the surface of a sphere is equal to the number of cubic centimeters in its volume, what is the diameter of the sphere ?

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Answer

Let r be the radius of the sphere.

According to question,

Surface area of sphere = Volume of sphere

⇒4πr2=43πr3⇒r2=r33⇒r3r2=3⇒r=3 cm.\Rightarrow 4πr^2 = \dfrac{4}{3}πr^3 \\[1em] \Rightarrow r^2 = \dfrac{r^3}{3} \\[1em] \Rightarrow \dfrac{r^3}{r^2} = 3 \\[1em] \Rightarrow r = 3\text{ cm}.

Diameter of sphere = 2r = 2 × 3 = 6 cm.

Hence, diameter of sphere = 6 cm.

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