what is the surface area of this sphere?\nround your answer to the nearest hundredth.\nimage of a sphere…

Explanation:

Step1: Find the radius of the sphere

The diameter of the sphere is given as 160 yd. The radius ( r ) is half of the diameter, so ( r=\frac{160}{2} = 80 ) yd.

Step2: Use the formula for the surface area of a sphere

The formula for the surface area ( S ) of a sphere is ( S = 4\pi r^{2} ). Substitute ( r = 80 ) into the formula: ( S=4\pi(80)^{2} ) First, calculate ( 80^{2}=6400 ). Then, ( 4\times6400 = 25600 ). So, ( S = 25600\pi ).

Step3: Calculate the numerical value

Using ( \pi\approx3.14159265 ), we get ( S\approx25600\times3.14159265 ). ( 25600\times3.14159265 = 80424.7712 ) (rounded to the nearest hundredth).

Answer:

80424.77