Question

If the volume of a sphere is numerically equal to its surface area, then find its diameter.

Answer 1

volume of a sphere is numerically equal to its surface area,

=) 4/3 * pi * r^3 = 4 * pi * r^2

=) r = 3

Hence d = 2r
= 2*3
= 6.

Hope it's helpful to u.

Answer 2

Given,

Volume of sphere is equal to its surface area numerically.

To find,

Diameter of the sphere.

Solution,

Let's see the formulae of spheres.

We know that , volume of sphere =   $\frac{4}{3}$ πr³

And the surface area of sphere =4πr²

In the question it's given that,

Volume of sphere = Surface area of sphere

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

Cancel out 4 and $\pi$ on both sides.

Then we get,

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

Therefore, r = 3.  

We know that diameter is twice the radius.

So, diameter = 2*r

Diameter = 2*3 = 6 cm

Hence, diameter of the sphere is 6 cm.