Question

if the volume and surface area of a sphere are numerically equal, then find its radius

Answer 1

Answer:

Step-by-step explanation:

Volume= surface area

4*22*r*r*r/7*3=4*22*r*r/7

(4/3*4)r³=r² (after pie cancelled)

(1/3)r³ = r²

r³= 3r²

(r/r)(3-2)=3

r = 3

Answer 2

Given:

The volume and surface area of a sphere are numerically equal.

To find:

The radius of the sphere.

Solution:

The radius of the sphere is 3 units.

To answer this question, we will follow the following steps:

As we know the surface area of a sphere having radius 'r' is given by using the formula:

$4\pi \: {r}^{2}$

Also,

its volume is given by:

$\frac{4}{3} \pi \: {r}^{3}$

Now,

As given in the question,

we have,

The surface area of sphere = volume of a sphere

So,

$4\pi {r}^{2} = \frac{4}{3} \pi \: {r}^{3}$

On solving the above, we get

${r}^{2} = \frac{1}{3} {r}^{3}$

$3 {r}^{2} = {r}^{3}$

$r = 3 \: units$

Hence, the radius of the given sphere is 3 units.