Question

Tomas draws a circle and dilates it on a photocopier using a scale factor of 3. If the original circle has a radius of 3 cm, what is the area of the dilated circle? Round your answer to the nearest tenth of a square centimeter.

The area of the dilated circle is approximately __ square centimeters.

Answer 1

To find the area of the dilated circle, we can follow these steps:

1. **Calculate the radius of the dilated circle:**
The original radius of the circle is 3 cm. If the circle is dilated using a scale factor of 3, the new radius will be:
\[
\text{New radius} = \text{Original radius} \times \text{Scale factor} = 3 \, \text{cm} \times 3 = 9 \, \text{cm}
\]

2. **Calculate the area of the dilated circle:**
The area \( A \) of a circle is given by the formula:
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle. Substituting the new radius into the formula gives:
\[
A = \pi (9 \, \text{cm})^2 = \pi \times 81 \, \text{cm}^2
\]

3. **Calculate \( \pi \times 81 \):**
Using an approximation for \( \pi \) as \( 3.14 \):
\[
A \approx 3.14 \times 81 \approx 254.34 \, \text{cm}^2
\]

4. **Round the result to the nearest tenth:**
\[
A \approx 254.3 \, \text{cm}^2
\]

Thus, the area of the dilated circle is approximately **254.3 square centimeters**.