You are told the circumference of the sphere. The circumference is the length of the circle around the widest part. You know the formula for the circumference of a circle in terms of radius, so you can find the radius of the sphere.
C = 2πr 496.12 yd = 2*3.14*r (496.12 yd)/(2*3.14) = r = 79 yd
Then the surface area of a sphere is given by ... A = 4πr^2 A = 4*3.14*(79 yd)² A = 78,386.96 yd²
_____ You can also find the area of a sphere in terms of its circumference. A = C²/π A = (496.12 yd)²/3.14 = 78,386.96 yd² . . . . same as above.
(The surface area in your problem statement, 3117.25 yd², corresponds to a sphere with a circumference of about 98.94 yd. The circumference given in the problem statement is almost 5 times that, which is why the area is almost 5²=25 times the area in your problem statement. This is a good one to ask your teacher about.)
