Question

what is the surface area of a sphere with a radius of 6 cm?
a. 678.24 cm²
b. 226.08 cm²
c. 452.16 cm²
d. 150.72 cm²

Explanation:

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

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

Step2: Substitute the given radius into the formula

Given \(r = 6\) cm and taking \(\pi=3.14\), we substitute into the formula: \(A = 4\times3.14\times6^{2}\).
First, calculate \(6^{2}=36\). Then, \(4\times3.14\times36=(4\times36)\times3.14 = 144\times3.14\).

Step3: Perform the multiplication

\(144\times3.14=(100 + 40+4)\times3.14=100\times3.14+40\times3.14 + 4\times3.14=314+125.6+12.56 = 452.16\) \(cm^{2}\).

Answer:

C. \(452.16\) \(cm^{2}\)