Question

what is the surface area of this sphere? round your answer to the nearest hundredth. 4.6 in square inches 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 \(r = 4.6\) inches. Substitute into the formula: \(A=4\pi(4.6)^{2}\).
First, calculate \((4.6)^{2}=4.6\times4.6 = 21.16\).
Then, \(A = 4\pi\times21.16\).
Since \(4\times21.16=84.64\), the formula becomes \(A = 84.64\pi\).

Step3: Calculate the numerical value

Using \(\pi\approx3.14159\), we have \(A=84.64\times3.14159\).
\(84.64\times3.14159=(80 + 4.64)\times3.14159=80\times3.14159+4.64\times3.14159\).
\(80\times3.14159 = 251.3272\), \(4.64\times3.14159=(4 + 0.64)\times3.14159=4\times3.14159+0.64\times3.14159=12.56636+2.0106176 = 14.5769776\).
\(A=251.3272+14.5769776=265.9041776\approx265.90\) (rounded to the nearest hundredth).

Answer:

\(265.90\)