Question

question 7 of 10
the axis of the sphere below is 16 units in length. what is the surface area of
the sphere?
a. 256π units²
b. 72π units²
c. 228π units²
d. cannot be determined

Explanation:

Step1: Recall the formula for the surface area of a sphere

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

Step2: Identify the radius of the sphere

The axis (diameter) of the sphere is given as \(16\) units. Since the radius \(r=\frac{d}{2}\) (where \(d\) is the diameter), then \(r = 16\div2=8\) units.

Step3: Substitute the radius into the surface - area formula

Substitute \(r = 8\) into \(S = 4\pi r^{2}\). We get \(S=4\pi\times8^{2}\). First, calculate \(8^{2}=64\). Then \(S = 4\pi\times64\). Since \(4\times64 = 256\), the surface area \(S = 256\pi\) units\(^{2}\).

Answer:

A. \(256\pi\) units\(^{2}\)