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.

Question

(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 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 2

this is wrong

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!