Problema Solution
The surface of a sphere varies directly as the square of radius. if the surface area is 36π square inches when the radius is 3 inches find the surface area when the radius is 4 inches.
Answer provided by our tutors
Let A be the surface area of a sphere that varies directly as the square of radius
A = k*r^2
for r = 3 in A = 36pi
36pi = k*3^2
36pi = 9k
k = 36pi/9
k = 4pi
thus A = 4pi*r^2
for r = 4 in
A = 4pi*4^2
A = 64pi in^2
the surface area when r = 4 in is 64 pi square inches.