Question

1.If surface area of sphere is equal to curved surface area of Hemisphere,
then radius of sphere is equal to two times of radius of hemisphere,
Are you agree ? Explain?​

Answer 1

$\pink { No, \: I \: doesn't \:agree }$

$Let \: Radius \: of \: Hemisphere = r \:units$

$Radius \: of \: the \: Sphere = R \: units$

$\pink { Surface \: area \: of \: sphere \:is }$

$\pink { equal \: to \: Surface \:area \:of \: }$

$\pink { hemisphere }$

$\implies 4 \pi (R)^{2} = 2 \pi r^{2}$

$\implies 2 R^{2} = r^{2}$

$\implies ( \sqrt{2} R )^{2} = r^{2}$

$\implies \sqrt{2} R = r$

Therefore.,

$\red { R } ≠ \green {2r }$

$\pink {Radius \: of \: Sphere }≠ \blue {two \: times \:of Radius \: of \: Hemisphere}$

•••♪

Answer 2

Step-by-step explanation:

No,Idoesn′tagree

Let \: Radius \: of \: Hemisphere = r \:unitsLetRadiusofHemisphere=runits

Radius \: of \: the \: Sphere = R \: unitsRadiusoftheSphere=Runits

\pink { Surface \: area \: of \: sphere \:is }Surfaceareaofsphereis

\pink { equal \: to \: Surface \:area \:of \: }equaltoSurfaceareaof

\pink { hemisphere }hemisphere

\implies 4 \pi (R)^{2} = 2 \pi r^{2}⟹4π(R)2=2πr2

\implies 2 R^{2} = r^{2}⟹2R2=r2

\implies ( \sqrt{2} R )^{2} = r^{2}⟹(2R)2=r2

\implies \sqrt{2} R = r⟹2R=r

Therefore.,

\red { R } ≠ \green {2r }R=2r

\pink {Radius \: of \: Sphere }≠ \blue {two \: times \:of Radius \: of \: Hemisphere}RadiusofSphere=twotimesofRadiusofHemisphere