Question

question 6 of 10
which expression gives the surface area of a sphere with radius r?
a. \\( \pi r ^ { 2 } \\)
b. \\( 4 \pi r ^ { 3 } \\)
c. \\( 4 \pi r ^ { 2 } \\)
d. \\( 4 r ^ { 2 } \\)

Explanation:

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

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

Step2: Analyze each option

• Option A: \(\pi r^{2}\) is the formula for the area of a circle, not the surface area of a sphere.
• Option B: \(4\pi r^{3}\) is not the formula for the surface area of a sphere. The volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\).
• Option C: \(4\pi r^{2}\) matches the formula for the surface area of a sphere.
• Option D: \(4r^{2}\) is missing the \(\pi\) factor which is essential in the formula related to circular - based (sphere in this case) geometric formulas.

Answer:

C. \(4\pi r^{2}\)