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

6

units

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8

units

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10

units

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12

units

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Solution

The correct option is A $6$ units
Let radius of sphere be 'r', then
Volume of sphere=surface area of sphere
$\Rightarrow \frac{4}{3} π R^{3} = 4 π r^{2} \Rightarrow \frac{r^{3}}{r^{2}} = 3 \Rightarrow r = 3$
$∴$ Diameter $= 2 \times 3 = 6$ units

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

The correct option is A 6 unitsLet radius of sphere be 'r', then Volume of sphere=surface area of sphere⇒43πR3=4πr2⇒r3r2=3⇒r=3∴Diameter=2×3=6 units

The correct option is A $6$ units
Let radius of sphere be 'r', then
Volume of sphere=surface area of sphere
$\Rightarrow \frac{4}{3} π R^{3} = 4 π r^{2} \Rightarrow \frac{r^{3}}{r^{2}} = 3 \Rightarrow r = 3$
$∴$ Diameter $= 2 \times 3 = 6$ units