Question

Find the radius of a sphere whose surface area is 49 pi cm square

Answer 1

Question

Find the radius of a sphere whose surface area is 49π cm²

Basic Concepts on Circles

Surface area and Total surface are of a Circle are the same.

S.A = 4πr²

Volume = $\mathsf{\frac{4}{3}}$ πr³

No of faces in a Sphere is 1

Answer

S.A of Sphere = 49π cm²

Formula for S.A of a sphere = 4πr²

Equating both,

4πr² = 49π

[π gets cancelled on both sides]

4r² = 49

r² = $\mathsf{\frac{49}{4}}$

r = $\mathsf{\sqrt{\frac{49}{4}}}$

r = $\mathsf{\frac{7}{2}}$ cm

Hence the radius is $\mathsf{\frac{7}{2}}$ cm

Answer 2

Answer: Radius (r) of sphere = $\bold{r\:=\:\frac{7}{2}\:cm}$

Step-by-step explanation:

We know that, (Useful Formulas)↓

• Surface Area of Sphere = $\bold{(4\:\times\pi\times\:r^{2})\:units^{2}}$

• Volume of Sphere = $\bold{(\frac{4}{3}\:\times\pi\times\:r^{3})\:units^{3}}$

To Find : Radius (r) of sphere.

Given : Surface Area = $\bold{49\:\times\:\pi}\:cm^{2}}$

Finding r :

Surface Area of Sphere = $\bold{(4\:\times\pi\times\:r^{2})\:units^{2}}$

But, Surface Area = $\bold{49\:\times\:\pi\:cm^{2}}$ ! (Given)

And, Surface Area = Surface Area

∴$\bold{(4\:\times\pi\times\:r^{2})\:units^{2}\:=\:49\:\times\:\pi\:cm^{2}}$

Putting values ;

$\implies\:\bold{(4\:\times\cancel{\pi}\times\:r^{2})\:units^{2}\:=\:49\:\times\:\cancel{\pi}\:cm^{2}}$

$\implies\:\bold{(4\:\times\cancel{\pi}\times\:r^{2})\:units^{2}\:=\:49\:\times\:\cancel{\pi}\:cm^{2}}$ (Pi and Pi cancel out)

$\implies\:\bold{(4\:\times\:r^{2})\:units^{2}\:=\:49\:cm^{2}}$ (Units Sq. and cm sq. cancel and left is cm.)

$\implies\:\bold{r^{2}\:=\:\frac{49}{4}\:cm}$

$\implies\:\bold{r\:=\:\sqrt{\frac{49}{4}}\:cm}$

$\implies\:\bold{r\:=\:\frac{\sqrt{49}}{\sqrt{4}}\:cm}$

$\implies\:\bold{r\:=\:\frac{7}{2}\:cm}$

∴Radius (r) of sphere = $\bold{r\:=\:\frac{7}{2}\:cm}$

Thanks!