Question 626129
Two spheres of the same density have a ratio of 4 to 9 in surface area.
 If the small sphere weighs 10 lb. what does the sphere weigh?
:
Surface area of the two spheres;
 r1= radius of the small sphere
 r2= radius of the larger sphere
{{{(4*pi*r1^2)/(4*pi*r2^2)}}} = {{{4/9}}}
cancel 4*pi
{{{(r1^2)/(r2^2)}}} = {{{4/9}}}
:
{{{(r1)/(r2)}}} = {{{sqrt(4/9)}}}
therefore
r1 = 2
r2 = 3
:
Vol is equiv of weight here
let w = weight of the larger sphere
{{{((4/3)pi*2^3)/((4/3)pi*3^3)}}} = {{{10/w}}}
Cancel {{{(4/3)pi}}} and you have:
{{{8/27}}} = {{{10/w}}}
cross multiply
8w = 27*10
w = {{{270/8}}}
w = 33.75, the weight of the larger sphere