the surface area of a sphere is 75 square centimeters, what is the volume of the sphere in cubic cm?
the surface area of a sphere is 75 square centimeters,
what is the volume of the sphere in cubic cm?
Formula:
The volume inside a sphere is: V=43πr3V=?.
The surface area of a sphere is: A=4πr2A=75 cm2.
VA=43πr34πr2VA=13⋅4π4π⋅r2r2⋅rVA=13⋅rV=13⋅r⋅A
Radius r:
A=4πr24πr2=A|:4πr2=A4π|√r=√A4πr=12⋅√Aπ
Volume V:
V=13⋅r⋅A|r=12⋅√AπV=13⋅12⋅√Aπ⋅AV=16⋅√A3π|A=75 cm2V=16⋅√(75 cm2)3πV=16⋅√753π cm3V=16⋅√134286.983234 cm3V=16⋅366.451883927 cm3V=61.0753139879 cm3
The volume of the sphere is 61.1 cm3