Open Response The exact circumference
of a circle is meters. What is the
approximate area of the circle? Use 314
for . Round to the nearest hundredth if
necessary.

Question

Open Response The exact circumference of a circle is $$ 34 \pi $$ meters. What is the approximate area of the circle? Use 314 for $$ \pi $$. Round to the nearest hundredth if necessary.

UpStudy AI · Accepted Answer

To find the approximate area of the circle given its circumference, we can follow these steps:

1. **Extract known conditions:**
   - The circumference $$ C $$ of the circle is given as $$ 34 \pi $$ meters.
   - We will use $$ \pi \approx 314 $$.

2. **Use the formula for circumference:**
   The formula for the circumference of a circle is given by:
   $$
   C = 2 \pi r
   $$
   where $$ r $$ is the radius of the circle.

3. **Solve for the radius $$ r $$:**
   We can rearrange the formula to solve for $$ r $$:
   $$
   r = \frac{C}{2 \pi}
   $$
   Substituting the given circumference:
   $$
   r = \frac{34 \pi}{2 \pi} = \frac{34}{2} = 17 \text{ meters}
   $$

4. **Calculate the area $$ A $$ of the circle:**
   The area of a circle is given by the formula:
   $$
   A = \pi r^2
   $$
   Substituting the radius we found:
   $$
   A = \pi (17)^2 = \pi \cdot 289
   $$

5. **Substituting $$ \pi $$ with 314:**
   $$
   A \approx 314 \cdot 289
   $$

6. **Perform the multiplication:**
   Now, we will calculate $$ 314 \cdot 289 $$:
   $$
   A \approx 314 \cdot 289
   $$

Let's calculate this value.
Calculate the value by following steps:
- step0: Calculate:
  $$314\times 289$$
- step1: Multiply the numbers:
  $$90746$$
The approximate area of the circle is $$ 90746 $$ square meters.

Since the problem does not require rounding to the nearest hundredth, the final answer is:

**The approximate area of the circle is $$ 90746 $$ square meters.**
The approximate area of the circle is 90,746 square meters.

Open Response The exact circumference
of a circle is meters. What is the
approximate area of the circle? Use 314
for . Round to the nearest hundredth if
necessary.

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Solución

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Latest Geometry Questions

Open Response The exact circumference of a circle is meters. What is the approximate area of the circle? Use 314 for . Round to the nearest hundredth if necessary.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

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Latest Geometry Questions

Open Response The exact circumference
of a circle is meters. What is the
approximate area of the circle? Use 314
for . Round to the nearest hundredth if
necessary.