Asphere with a 4-in. radius is being plated with silver for a cost of $30. if gold plating costs 75% more than silver plating, how much will it cost to gold-plate a sphere with radius 6 in.?

Step 1
find the surface area of a sphere
the surface area of a sphere=4*pi*r²
for r=4 in
surface area=4*pi*4²> 64*pi in²

step 2
find the surface area of a sphere for r=6 in
surface area=4*pi*6²> 144*pi in²

step 3
if for 64*pi in²> the cost of silver plating is $30
144*pi in²> x
x=144*pi*30/(64*pi)> x=$67.5

the gold plating costs 75% more than silver plating
so
$67.5*1.75=$118.125

the answer is
to gold-plate a sphere with radius 6 in the cost is $118.125