Questions: A globe is 41.177 feet in diameter. Find its exact circumference (distance around) and then approximate its circumference. The exact circumference of the globe is (Simplify your answer. Type an exact answer in terms of π.)

A globe is 41.177 feet in diameter. Find its exact circumference (distance around) and then approximate its circumference.

The exact circumference of the globe is (Simplify your answer. Type an exact answer in terms of π.)

Transcript text: A globe is 41.177 feet in diameter. Find its exact circumference (distance around) and then approximate its circumference. The exact circumference of the globe is $\square$ $\square$ (Simplify your answer. Type an exact answer in terms of $\pi$.)

Solution

Solution Steps

To find the circumference of a globe given its diameter, we use the formula for the circumference of a circle, which is $ C = \pi \times d $, where $ d $ is the diameter. For the exact circumference, we will leave the answer in terms of $\pi$. For the approximate circumference, we will use the value of $\pi \approx 3.14159$.

Step 1: Determine the Exact Circumference

To find the exact circumference of a globe with a diameter of 41.177 feet, we use the formula for the circumference of a circle: \[ C = \pi \times d \] Substituting the given diameter: \[ C = \pi \times 41.177 \]

Step 2: Determine the Approximate Circumference

To find the approximate circumference, we use the value of $\pi \approx 3.14159$: \[ C \approx 3.14159 \times 41.177 \] \[ C \approx 129.3614 \]