Question 1203309




Surface area of a sphere: 

{{{ A=4*pi*r^2}}}

let altitude be {{{ h }}}and diameter {{{ d}}}


given: 

{{{ h=2cm}}}


The area of a spherical zone is {{{ A=50.265cm^2}}}


using the formula {{{ A=2pi*rh}}} where {{{ h}}} is the height of the spherical layer and {{{ r}}} is the radius of the sphere, substitute given


{{{ 50.265cm^2=2pi*r*2cm}}} ....solve for {{{r}}}

{{{ r=50.265cm^2/(2pi*2cm)}}}.....simplify

{{{ r=50.265cm/(4pi)}}}

{{{ r=50.265cm/(4pi)}}}

{{{ r=3.9999616072570596cm}}}

{{{ r=4cm}}}


then, surface area of a sphere is: 

{{{ A=4*pi*(4cm)^2}}}

{{{ A=4*pi*16cm^2}}}

{{{ A=64pi*cm^2}}}

{{{ A=201.062cm^2}}}