Question

what is the surface area of this sphere?
round your answer to the nearest hundredth.
image of a sphere with diameter 160 yd
blank square yards

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