Question

in the volume of the sphere is divided by its surface area the resultant is 27 cm .the radius of the sphere is 3 power n .the value of n is ??​

Answer 1

Answer:

The value of n is 4.

Explanation:

Given :

• If the volume of the sphere is divided by its surface area the resultant is 27 cm.
• The radius of the sphere is 3ⁿ.

To find :

the value of n

Solution :

We know,

Volume of sphere =  $\sf \dfrac{4}{3} \pi r^3$

Surface area of sphere = 4πr²

According to the question,

$\sf \dfrac{volume \ of \ the \ sphere}{surface \ area \ of \ sphere}=27 \\\\ \sf \dfrac{\dfrac{4}{3}\pi r^3}{4\pi r^2}=27 \\\\ \sf \dfrac{r}{3}=27 \\\\ \sf r=27 \times 3 \\\\ \sf r=81$

The radius of the sphere is 81 cm.

Given, the radius of the sphere is 3ⁿ.

3ⁿ = 81

⇒ 3ⁿ = 3⁴

⇒ n = 4

∴ The value of n is 4.