Question

select the correct answer.
the surface area of a sphere is approximately 145.2 square feet. what is the diameter of the sphere?
a. 4.8 feet
b. 6.8 feet
c. 9.6 feet
d. 3.4 feet

Explanation:

Step1: Recall the surface area formula of a sphere

The surface area formula of a sphere is \(S = 4\pi r^{2}\), where \(S\) is the surface area and \(r\) is the radius. Given \(S=145.2\) square feet.

Step2: Solve for the radius \(r\)

Substitute \(S = 145.2\) into the formula \(145.2=4\pi r^{2}\). First, \(\pi\approx3.14\), then \(r^{2}=\frac{145.2}{4\times3.14}=\frac{145.2}{12.56} = 11.56\). Take the square - root of both sides, \(r=\sqrt{11.56}=3.4\) feet.

Step3: Calculate the diameter \(d\)

Since the diameter \(d = 2r\), and \(r = 3.4\) feet, then \(d=2\times3.4 = 6.8\) feet.

Answer:

B. 6.8 feet