Question

The volume and surface area of a sphere are numerically equal find the diameter of the sphere

Answer 1

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$<b>Answer</b>$

Diameter = 6 unit

$<b>Step-by-step explanation</b>$

Surface area of a sphere = $4π3^2$

Volume of a sphere = $\frac{4}{3}πr^3$

$<b>Given that,</b>$

Surface area of a sphere = volume of a sphere

$4πr^2$ = $\frac{4}{3}πr^3$

$<b><font color="lightpink">πr^2 and πr^2 will be cancelled from both the sides.</font></b>$

Then, 4 = $\frac{4}{3}r^3$

4 × 3 = 4r

12 = 4r

$\frac{12}{4}$ = r

3 = r

Radius = 3

Diameter = 2r

Diameter = 2 × 3

Therefore, diameter = 6 unit.

$<b><font color="yellow">Note :</font></b>$ If unit is not given, then you should write just 'unit' after your answer.

Thanks..!

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