Question

If the surface area and the volume of a sphere is equal. Then calculate the diameter of the sphere.

Answer 1

¡ƒ тнε รuяƒคcε คяεค คหd тнε vσłuмε σƒ ค รpнεяε ¡ร εquคł.тнεห cคłcułคтε тнε d¡คмεтεя σƒ тнε รpнεяε.

ร๏ℓนт¡๏ภ:

รuяƒคcε คяεค σƒ รpнεяε = 4 πя^2

vσłuмε σƒ รpнεяε = 4/3 πя^3

g¡vεห,

รuяƒคcε คяεค σƒ รpнεяε = vσłuмε σƒ รpнεяε

⇒ 4 πя^2 = 4/3 πя^3

⇒ я/3 = 1

⇒ я = 3

нεหcε, яคd¡uร ¡ร 3.

หσω, ωε кหσω тнคт d¡คмεтεя ¡ร dσuЪłε σƒ яคd¡uร.

รσ, 3 × 2 = 6

нεหcε, тнε d¡คмεтεя σƒ тнε รpнεяε ¡ร 6.

нσpε ¡т нεłpร!

Answer 2

$\mathbb{\pink{\huge{Hello\:Mate!!!}}}$

$<b>Answer</b>$

Diameter = 6 unit

$<b>Step-by-step explanation</b>$

Surface area of a sphere = $4πr{}^{2}$

Volume of a sphere = $\frac{4}{3}πr{}^{2}$

$<b>Given that,</b>$

Surface area of a sphere = volume of a sphere

$4πr{}^{2}$ = $\frac{4}{3}πr{}^{3}$

$<b><font color="lightpink">4πr^2 will be cut on both sides.</font></b>$

Then, $4πr{}r^{2}$ = $\frac{4}{3}πr{}^{3}$ will be,

4 = $\frac{4}{3}r$

4 × 3 = 4r

12 = 4r

$\frac{12}{4}$ = r

3 = r

Radius = 3

Diameter = 2r

Then, diameter = 2 × 3

Diameter = 6 unit.

Hope it will work for you my dear sista!

Thanks..!

With♥️