Question

the radius r of a sphere is 7.3 cm. calculate the spheres surface area a. use the value 3.14 for π, and round your answer to the nearest tenth. a = □ cm²

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 \(R = 7.3\) cm and \(\pi=3.14\), substitute into the formula:
\(A = 4\times3.14\times(7.3)^{2}\)
First, calculate \((7.3)^{2}=7.3\times7.3 = 53.29\)
Then, \(A = 4\times3.14\times53.29\)
\(4\times3.14 = 12.56\)
So, \(A=12.56\times53.29\)
\(12.56\times53.29=(12 + 0.56)\times53.29=12\times53.29+0.56\times53.29\)
\(12\times53.29 = 639.48\)
\(0.56\times53.29=(0.5 + 0.06)\times53.29=0.5\times53.29+0.06\times53.29=26.645+3.1974 = 29.8424\)
\(A=639.48+29.8424 = 669.3224\)

Step3: Round to the nearest tenth

Rounding \(669.3224\) to the nearest tenth. The digit in the hundredth place is \(2\), so we keep the digit in the tenth place as it is.

Answer:

\(669.3\)