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
