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

this is wrong

Answer 2

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

The original circle has a radius of 3 cm. When dilated by a scale factor of 3, the new radius \( r \) can be calculated as follows:

\[
r = \text{original radius} \times \text{scale factor} = 3 \, \text{cm} \times 3 = 9 \, \text{cm}
\]

Next, we calculate the area \( A \) of the circle using the formula for the area of a circle, which is:

\[
A = \pi r^2
\]

Substituting the new radius into the formula:

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

Now, calculating the area using the approximate value of \(\pi \approx 3.14\):

\[
A \approx 3.14 \times 81 \approx 254.34 \, \text{cm}^2
\]

Rounding this to the nearest tenth, we get:

\[
A \approx 254.3 \, \text{cm}^2
\]

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

Answer 3

Let's go through the calculations step by step to ensure we get the correct answer for the area of the dilated circle.

1. **Determine the original radius**: The original radius of the circle is given as 3 cm.

2. **Calculate the new radius after dilation**: When the circle is dilated by a scale factor of 3, the new radius \( r \) is calculated as follows:

\[
r = \text{original radius} \times \text{scale factor} = 3 \, \text{cm} \times 3 = 9 \, \text{cm}
\]

3. **Calculate the area of the dilated circle**: The area \( A \) of a circle is given by the formula:

\[
A = \pi r^2
\]

Substituting the new radius into the formula:

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

4. **Use the approximate value of \(\pi\)**: Using \(\pi \approx 3.14\),

\[
A \approx 3.14 \times 81 = 254.34 \, \text{cm}^2
\]

5. **Round to the nearest tenth**:

\[
A \approx 254.3 \, \text{cm}^2
\]

The calculations appear to be correct according to the method outlined above. Hence, the area of the dilated circle is approximately **254.3 square centimeters**. If your answer differs from this, please advise on any specific points of confusion so I can clarify!