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Problem 911

# 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?

Expert verified
The surface area of the Earth is approximately 2,011,428.32 square miles.
See the step by step solution

## 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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