Question

if the volume & surface area of the sphere is equal then the radius is​

Answer 1

Step-by-step explanation:

then the radius is 3.

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Answer 2

$\begin{gathered}\begin{gathered}\bf \:Given - \begin{cases} &\sf{Volume_{(sphere)} = Surface Area_{(sphere)}} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:To\: find - \begin{cases} &\sf{radius_{(sphere)}}  \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\Large{\bold{{\underline{Formula \: Used - }}}}  \end{gathered}$

$1. \: \: \: \boxed{ \tt{Volume_{(sphere)} = \dfrac{4}{3}\pi \: {r}^{3} }}$

$2. \: \: \: \boxed{ \tt{Surface Area_{(sphere)} \: = \: 4 \: \pi \: {r}^{2} }}$

$\large\underline{\bold{Solution-}}$

Let radius of sphere be 'r' units.

According to statement,

$\sf \: Volume_{(sphere)} \: = \: Surface Area_{(sphere)}$

$\sf \: \dfrac{ \cancel4}{3} \: \cancel\pi \: {r}^{3} \: = \: \cancel4 \: \cancel\pi \: {r}^{2}$

$\: \: \bf \: \: r \: = \: 3 \: units$

Additional Information :-

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length ²+breadth ²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²