Question

If the volume of a sphere is divided bybits surface area the result is 27cm.the radius of sphere is?

Answer 1

Given :

If the volume of a sphere is divided bybits surface area the result is 27cm.

To find :

Radius of sphere

Solution :

Volume of sphere is given by,

$\longmapsto\displaystyle\bold{Volume \ of \ sphere = \dfrac{4}{3} \ \pi r^3}$

Surface area of sphere is given by,

$\longmapsto\diplaystyle\bold{Surface \ area \ of \ sphere = 4 \pi r^2 }$

So according to question,

$\longmapsto\sf \ \ \dfrac{\dfrac{4}{3} \pi r^3}{4 \pi r^2} = 27 \\\\\\ \longmapsto\sf \ \ \dfrac{4}{3} \pi r^3 \times \dfrac{1}{4 \pi r^2} = 27 \\\\\\ \longmapsto\sf \ \ \dfrac{r}{3} = 27 \\\\\\ \ \ \longmapsto\underline{\boxed{\bold{r = 81 \ cm }}} \\\\\\\\ \therefore \ \ \overline{\underline{\boxed{\textsf{\ Radius of sphere = 81 cm \ }}}}$

Answer 2

Answer:

Radius of sphere is 81cm.

Step-by-step explanation:

• REMEMBER

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

Surface Area of sphere = $4 \pi{r}^{2}$

• SOLUTION

According to the Question ,

$\rm\frac{Volume \: of \: sphere }{Surface \: Area \: of \: sphere}$ = 27cm

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

$\implies \: \frac{ \cancel4}{ 3} \cancel\pi \: {r} \: ^{ \cancel3} \times \frac{1}{ \cancel4 \: \cancel \pi \: \: \cancel{{r}^{2} }} = 27cm$

$\implies \frac{r}{3} = 27cm$

$\implies \: r = 3 \times 27cm$

$\implies \: r = 81cm$

• ANSWER

Radius of sphere is 81cm.

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