Question

the radius r of a sphere is 3.9 mm. calculate the spheres surface area a. use the value 3.14 for π, and round your answer to the nearest tenth. a = mm²

Explanation:

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

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

Step2: Substitute the given values

Given \(R = 3.9\) mm and \(\pi=3.14\). First, calculate \(R^{2}\): \(R^{2}=(3.9)^{2}=3.9\times3.9 = 15.21\). Then substitute into the formula: \(A = 4\times3.14\times15.21\).

Step3: Perform the multiplications

\(4\times3.14 = 12.56\), then \(12.56\times15.21=12.56\times(15 + 0.21)=12.56\times15+12.56\times0.21\).
\(12.56\times15=(12 + 0.56)\times15=12\times15+0.56\times15 = 180+8.4 = 188.4\), \(12.56\times0.21=(12 + 0.56)\times0.21=12\times0.21+0.56\times0.21=2.52 + 0.1176=2.6376\).
\(188.4+2.6376 = 191.0376\).

Answer:

\(191.0\)