Question

the radius ( r ) of a sphere is ( 5.8 mathrm{~cm} ). calculate the spheres surface area ( a ).
use the value ( 3.14 ) for ( pi ), and round your answer to the nearest tenth.

Explanation:

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

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

Step2: Substitute the given values

Given \(R = 5.8\) cm and \(\pi=3.14\), substitute into the formula:
\(A = 4\times3.14\times(5.8)^{2}\)
First, calculate \((5.8)^{2}=5.8\times5.8 = 33.64\)
Then, \(4\times3.14\times33.64=12.56\times33.64\)
\(12.56\times33.64=(12 + 0.56)\times33.64=12\times33.64+0.56\times33.64\)
\(12\times33.64 = 403.68\), \(0.56\times33.64=(0.5 + 0.06)\times33.64=0.5\times33.64+0.06\times33.64=16.82+2.0184 = 18.8384\)
\(403.68+18.8384 = 422.5184\)

Answer:

\(422.5\)