Question

the radius r of a sphere is 6.7 m. calculate the spheres surface area a. use the value 3.14 for π, and round your answer to the nearest tenth.

Explanation:

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

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

Step2: Substitute the given values into the formula.

We are given that \( R = 6.7 \, \text{m} \) and \( \pi \approx 3.14 \). Substituting these values into the formula, we get:
\( A = 4\times3.14\times(6.7)^{2} \)
First, calculate \( (6.7)^{2} \):
\( 6.7\times6.7 = 44.89 \)
Then, multiply by \( 4\times3.14 \):
\( 4\times3.14 = 12.56 \)
Now, multiply \( 12.56 \) by \( 44.89 \):
\( 12.56\times44.89 = 12.56\times44 + 12.56\times0.89 \)
\( 12.56\times44 = 552.64 \)
\( 12.56\times0.89 = 11.1784 \)
Adding these two results together: \( 552.64 + 11.1784 = 563.8184 \)

Step3: Round the answer to the nearest tenth.

To round \( 563.8184 \) to the nearest tenth, we look at the hundredth place, which is \( 1 \). Since \( 1 < 5 \), we round down. So, \( 563.8184 \approx 563.8 \)

Answer:

\( 563.8 \)