Problema Solution
The surface area of a sphere (A) varies directly as the square of the radius of the sphere. To cover a 4 inch diameter baseball, it takes about 50 square inches of leather. Find the model that relates surface area to the radius. Use it to find the surface area of a playground ball that has a 10 inch radius.
Answer provided by our tutors
The surface area of a sphere (A) varies directly as the square of the radius of the sphere
A = k*r^2, where k is a constant
To cover a 4 inch diameter baseball, it takes about 50 square inches of leather means that for r = 4 in, A = 50 in^2
k*4^2 = 50
k = 50/16
k = 25/8
A = (25/8)*r^2 is the model
for r = 10 in we have
A = (25/8)*10^2
A = 312.5 in^2