Question

what is the surface area of this sphere? round your answer to the nearest hundredth. 17 cm square centimeters submit

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 \(r = 17\) cm. Substitute \(r = 17\) into \(A = 4\pi r^{2}\):
\(A=4\pi\times(17)^{2}\)
First, calculate \((17)^{2}=289\). Then \(A = 4\pi\times289\).
Since \(4\times289 = 1156\), the formula becomes \(A=1156\pi\).

Step3: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(A = 1156\times3.14159\).
\(1156\times3.14159=1156\times(3 + 0.14159)=1156\times3+1156\times0.14159\)
\(1156\times3 = 3468\), \(1156\times0.14159=(1000 + 100+ 50+6)\times0.14159\)
\(1000\times0.14159 = 141.59\), \(100\times0.14159=14.159\), \(50\times0.14159 = 7.0795\), \(6\times0.14159=0.84954\)
\(141.59+14.159+7.0795 + 0.84954=163.67804\)
\(3468+163.67804 = 3631.67804\approx3631.68\)

Answer:

\(3631.68\)