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Chapter 52: Chapter 52

Problem 911

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The surface area of a sphere is \(4 \pi \mathrm{r} 2\), where \(\mathrm{r}\) is the radius of the sphere. Assuming that the diameter of the earth is 800 miles and \(\pi=22 / 7\), what is the surface area of the earth?

Short Answer

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The surface area of the Earth is approximately 2,011,428.32 square miles.
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Find the radius of the Earth#

Given the diameter of the Earth is 800 miles, we can find the radius by dividing the diameter by 2: \[r = \frac{diameter}{2}\] \[r = \frac{800}{2} = 400 \, miles\]

Step 2: Substitute values into the surface area formula#

Now that we have the radius, we can substitute the values of the radius and \(\pi\) into the surface area formula: \[A = 4 \pi r^2\] \[A = 4 \times \frac{22}{7} \times (400)^2\]

Step 3: Solve for the surface area of the Earth#

Perform the calculation to find the surface area: \[A = 4 \times \frac{22}{7} \times (400)^2\] \[A = 4 \times \frac{22}{7} \times 160000\] \[A = 4 \times 22 \times 22857.14\] (approximating \(\frac{160000}{7}\)) \[A = 88 \times 22857.14\] \[A \approx 2,011,428.32 \, square \, miles\] The surface area of the Earth is approximately 2,011,428.32 square miles.

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