Question

If the volume of a sphere is divided by its surface area the result is 27cm find the diameter of the sphere

Answer 1

AnswEr:

$:\implies\sf\; Volume \;of \;Sphere = \frac{4}{3}\pi\;r^3 h$

$:\implies\sf\; Surface \; area \;of \;sphere\; = 4\pi\;r^2$

$\rule{150}3$

We have Given that if the volume of a sphere is divided by its surface area, the result is 27cm.

Therefore,

$:\implies\sf\; \dfrac{4\pi\;r^3}{4\pi\;r^2}$

$:\implies\sf\; \dfrac{4 r}{12} = 27$

$:\implies\sf\; r = \dfrac{27}{4}$

$:\implies\large\boxed{\sf{\blue{ r = 81}}}$

We know that $\sf\; Diameter = \dfrac{r}{2}$

So, Diameter = $\sf\dfrac{81}{2}$

$:\implies\large\boxed{\sf{\blue{Diameter = 40.5}}}$

$\rule{150}3$

Answer 2

Answer:

162 cm

Step-by-step explanation:

Volume of the circle=$\frac{4}{3} \pi r^3$

CSA of the circle=$4\pi r^2$

A/q,

$\frac{\frac{4}{3} \pi r^3}{4\pi r^2} =27$

(here 4 cancels 4 from 4/3, π cancels π and r² cancels r² from r³)

$\frac{1}{3} r=27$

$r=27*3=81$

Now, the diameter = 2r.

Diameter=2*81=162 cm.