Question
Rupert is copying some files from his computer to a compact disc, like the one shown above.
If the diameter of the compact disc is 120 millimeters, what is the approximate area ignoring the center hole? (Use 3.14 for .)
A.
753.6 mm2
B.
45,216 mm2
C.
11,304 mm2
D.
376.8 mm2
Answers
GPT-4o mini
To find the area of a compact disc (ignoring the center hole), we can use the formula for the area of a circle:
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle and \( \pi \) is approximately 3.14.
1. First, calculate the radius from the diameter:
\[
r = \frac{diameter}{2} = \frac{120 \text{ mm}}{2} = 60 \text{ mm}
\]
2. Now, plug the radius into the area formula:
\[
A = 3.14 \times (60 \text{ mm})^2
\]
3. Calculate \( (60 \text{ mm})^2 \):
\[
(60 \text{ mm})^2 = 3600 \text{ mm}^2
\]
4. Now calculate the area:
\[
A = 3.14 \times 3600 \text{ mm}^2
\]
5. Perform the multiplication:
\[
A = 11,304 \text{ mm}^2
\]
Therefore, the approximate area of the compact disc (ignoring the center hole) is:
**C. 11,304 mm²**
\[
A = \pi r^2
\]
where \( r \) is the radius of the circle and \( \pi \) is approximately 3.14.
1. First, calculate the radius from the diameter:
\[
r = \frac{diameter}{2} = \frac{120 \text{ mm}}{2} = 60 \text{ mm}
\]
2. Now, plug the radius into the area formula:
\[
A = 3.14 \times (60 \text{ mm})^2
\]
3. Calculate \( (60 \text{ mm})^2 \):
\[
(60 \text{ mm})^2 = 3600 \text{ mm}^2
\]
4. Now calculate the area:
\[
A = 3.14 \times 3600 \text{ mm}^2
\]
5. Perform the multiplication:
\[
A = 11,304 \text{ mm}^2
\]
Therefore, the approximate area of the compact disc (ignoring the center hole) is:
**C. 11,304 mm²**