Question

If the volume and surface area of a sphere are numerically equal, then its radius is
a)1 unit
b) 2 unit
c) 3 unit
d) 4 unit​

Answer 1

radius is 3 unit

I hope it's helpful for you

Answer 2

$\bf \: \underline{Given} :$ ↴

$\sf \: The \: volume \: and \: surface \: area \: of \: a \: sphere \: are \: numerically \: equal.$

$\bf \: \underline{To \: find} :$ ↴

$\sf \: We \: have \: to \: find \: its \: radius.$

$\bf \: \underline{\underline{Solution}} :$ ↴

$\sf \: Let \: the \: radius \: of \: the \: sphere \: be \: x.$

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\sf\: We \: know \: that, \begin{cases} &\sf{\sf Surface \: area \: of \: sphere = 4 \pi r ^{2}} \\ \\ &\sf{{\sf Volume \: of \: sphere = \dfrac{4}{3} \pi r^{3} }} \end{cases}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\sf \: According \: to \: question,$

$\sf \: \underline{ Surface \: area = Volume}$

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

$\sf \: \implies \: 4 \pi \: r \times r= \dfrac{4}{3} \pi \: r \times r \times r$

$\sf \: \implies \: 4 = \dfrac{4}{3} \: r$

$\sf \: \implies \: r = 4 \times \dfrac{3}{4}$

$\sf \: \implies \: r = 3$

$\underline{ \boxed{ \pink{ \sf \: Hence, Radius \: is \: 3 \: units}}}$

$\bf \: \underline{More \: to \: know \: about \: sphere},$

Sphere is a three dimensional shape.

A Sphere has all points of its boundary equidistant from a common point called its centre.

The equal distance is called its radius.

The extent of the sphere is called the diameter of the sphere.