Question

3. The surface area of a sphere same as the CSA
of a right circular cylinder whose height and
diameter are 4cm each Find the radius of the Sphere


​

Answer 1

✫ The radius of the sphere is 2 cm✫

Step-by-step explanation:

Given:-

• Height = 4 cm
• Diameter = 4 cm

To find:-

• Radius of sphere

Required Formula:-

• Surface area of sphere = 4πr²
• CSA of right circular cylinder = 2πrh

Solution:-

Where,

• Radius = d/2 =  4/2 = 2 cm

Putting the values,

$\\ :\implies\sf{CSA = 2 \times \pi \times 2\times 4}\\ \\ :\implies\sf{CSA=2\times \pi \times 8}\\ \\ :\implies\sf{CSA=16\times \pi}$

As here the surface area of a sphere same as the csa of right circular cylinder,so

$\\ :\implies\sf{4\pi r^2=\pi\times 16}\\ \\ :\implies\sf{r^2=\cancel{\frac{16}{4}}} \\ \\ :\implies\sf{r^2 = 4}\\ \\ :\implies\sf{r=\sqrt{4}}\\ \\ :\implies\underline{\boxed{\pink{\mathfrak{r = 2}}}}\;\bigstar$

• ∴ Hence,the radius of the sphere is 2 cm.

Answer 2

Given:-  

• Height = 4cm

• Diameter = 4cm

To find:-  

• Radius

Solution:-  

Firstly we have to find the CSA of a cylinder

• $\sf{Radius\:=\:\dfrac{Diameter}{2}\:=\:\dfrac{4}{2}\:=\:2cm}$

$\sf{\longmapsto\:CSA\:=\:2\pi rh}$

$\sf{\longmapsto\:CSA\:=\:2\:\times\:\pi \:\times\:2\:\times\:4}$

$\sf{\longmapsto\:CSA\:=\:2\:\times\:\pi \:\times\:8}$

$\sf{\longmapsto\:CSA\:=\:16\:\times\:\pi }$

• On the given data, the surface area of a sphere = the CSA of the right circular cylinder,

$\sf{\longmapsto\:Surface\:Area\:_{(Sphere)}\:=\:CSA\:_{(Right\:circular\:cylinder)}}$

$\sf{\longmapsto\:4\pi r^{2}\:=\:\pi \:\times\:16}}$

$\sf{\longmapsto\:(Radius)^{2}\:\:=\:\dfrac{16}{4}}$

$\sf{\longmapsto\:(Radius)^{2}\:\:=\:4}$

$\sf{\longmapsto\:Radius\:=\:\sqrt{4} }$

$\sf{\longmapsto\:Radius\:=\:2cm}$

$\texttt{\underline{Therefore\:the\:radius\:of\:the\:sphere\:is\:2cm\:.}}$