Question

Tomaz 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. (1 point) The area of the dilated circle is approximately square centimeters.

Answer 1

To find the area of the dilated circle, we first need to determine the new radius after dilation.

The original radius of the circle is 3 cm. When we dilate this circle using a scale factor of 3, the new radius can be calculated as follows:

\[
\text{New radius} = \text{Original radius} \times \text{Scale factor} = 3 \, \text{cm} \times 3 = 9 \, \text{cm}
\]

Next, we can calculate the area of the circle using the formula for the area of a circle:

\[
\text{Area} = \pi r^2
\]

where \( r \) is the radius of the circle. Substituting the new radius into the formula gives:

\[
\text{Area} = \pi (9 \, \text{cm})^2 = \pi \times 81 \, \text{cm}^2
\]

Calculating this gives:

\[
\text{Area} \approx 3.14159 \times 81 \approx 254.47 \, \text{cm}^2
\]

Rounding this value to the nearest tenth, we find:

\[
\text{Area} \approx 254.5 \, \text{cm}^2
\]

Thus, the area of the dilated circle is approximately **254.5 square centimeters**.