Question

1. determine the surface area of a sphere with a radius of 6 cm.

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 \(r = 6\space cm\), substitute \(r\) into the formula: \(A=4\pi\times(6)^{2}\).
First, calculate \((6)^{2}=36\). Then \(A = 4\pi\times36\).

Step3: Calculate the value

\(4\times36 = 144\), so \(A=144\pi\space cm^{2}\). If we take \(\pi\approx3.14\), then \(A = 144\times3.14=452.16\space cm^{2}\).

Answer:

If using the exact form: \(144\pi\space cm^{2}\). If using \(\pi\approx3.14\): \(452.16\space cm^{2}\)