Question 1203307


Surface area of a sphere: 

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


let altitude be {{{h}}} and diameter {{{d}}}
given ratio is {{{1:5}}}


so, {{{h/d=1/5}}}


{{{h=d/5}}}

{{{r=d/2 }}}=> {{{h=(d/2)/5=d/10}}}


The area {{{A}}} of a spherical zone can be calculated using the formula 


{{{A=2Ï€rh }}}

where {{{h }}}is the height of the spherical layer and {{{r}}} is the radius of the sphere.


if  the area of the zone is {{{80pi}}}, we have

{{{80pi=2pi*rh}}}...simplify

{{{40=rh}}}.....substitute {{{h}}}

{{{40=r(r/10)}}}

{{{400=r^2}}}

{{{r=sqrt(400)}}}

{{{r=20}}}


then, surface area of a sphere is: 

{{{A=4*pi*20^2}}}

{{{A=4*pi*400}}}

{{{A=1600pi}}}