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

Question

The area of the dilated circle is approximately _ square centimeters

Answer 1

To find the area of the dilated circle, we start with the original circle which has a radius of 3 cm.

The area \( A \) of a circle is given by the formula: \[ A = \pi r^2 \] where \( r \) is the radius of the circle.

1. Calculate the area of the original circle: \[ A_{\text{original}} = \pi (3 , \text{cm})^2 = \pi \times 9 , \text{cm}^2 = 9\pi , \text{cm}^2 \]

2. Apply the scale factor of 3 to the radius of the circle: \[ \text{New radius} = 3 \times 3 , \text{cm} = 9 , \text{cm} \]

3. Calculate the area of the dilated circle using the new radius: \[ A_{\text{dilated}} = \pi (9 , \text{cm})^2 = \pi \times 81 , \text{cm}^2 = 81\pi , \text{cm}^2 \]

4. Now, we need to approximate the area in square centimeters. Using \( \pi \approx 3.14 \): \[ A_{\text{dilated}} \approx 81 \times 3.14 = 254.34 , \text{cm}^2 \]

5. Round the area: \[ A_{\text{dilated}} \approx 254.3 , \text{cm}^2 \]

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