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Mathematics

If the volume and the surface area of a sphere are numerically the same, then its radius is:

  1. 1 unit

  2. 2 units

  3. 3 units

  4. 4 units

Mensuration

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Answer

Let radius of sphere be r cm.

Given,

Volume of sphere = Surface area of sphere

⇒43πr3=4πr2⇒4πr3=3×4πr2⇒4r3=12×r2⇒r3=124×r2⇒r3r2=3⇒r=3 units.\Rightarrow \dfrac{4}{3} π\text{r}^3 = 4π\text{r}^2 \\[1em] \Rightarrow 4π\text{r}^3 = 3 \times 4π\text{r}^2 \\[1em] \Rightarrow 4\text{r}^3 = 12 \times \text{r}^2 \\[1em] \Rightarrow \text{r}^3 = \dfrac{12}{4} \times \text{r}^2 \\[1em] \Rightarrow \dfrac{\text{r}^3}{\text{r}^2} = 3 \\[1em] \Rightarrow \text{r} = 3 \text{ units.}

Hence, option 3 is the correct option.

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