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Maths-

General

Easy

Question

The volume of a sphere is given by the formula $V equals 4 over 3 pi r cubed$ , where r is the radius of the sphere. Which of the following gives the radius of the sphere in terms of the volume of the sphere?

$\frac{4 π}{3 V}$
$\frac{3 V}{4 π}$
$\sqrt[3]{\frac{4 π}{3 V}}$
$\sqrt[3]{\frac{3 V}{4 π}}$

hint Hint:

Hint:
Volume of sphere is given by $V equals 4 over 3 pi r cubed text . end text$

The correct answer is: $cube root of fraction numerator 3 V over denominator 4 pi end fraction end root$

Explanation:

We have given volume of sphere as $V equals 4 over 3 pi 7 cubed$

We have to find the radius in terms of volume

Step 1 of 1:
We have volume of sphere as . $V equals 4 over 3 pi r cubed$

Now multiply both hand side with $fraction numerator 3 over denominator 4 pi end fraction$

So,

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator 3 over denominator 4 pi end fraction cross times V equals fraction numerator 3 over denominator 4 pi end fraction cross times 4 over 3 pi r cubed end cell row cell fraction numerator 3 v over denominator 4 pi end fraction equals r cubed end cell end table$

Now, take cube root both side

$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator 3 over denominator 4 pi end fraction cross times V equals fraction numerator 3 over denominator 4 pi end fraction cross times 4 over 3 pi r cubed end cell row cell cube root of fraction numerator 3 V over denominator 4 pi end fraction end root equals cube root of r cubed end root end cell row cell r equals cube root of fraction numerator 3 V over denominator 4 pi end fraction end root end cell end table$

Hence, Option D is correct.

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