Question
If a pizza with a 24-inch diameter is cut into 12 equal pieces, then what is the length of the crust along the edges that are cut
Answers
GPT-4o mini
To find the length of the crust along the edges that are cut when a pizza with a 24-inch diameter is cut into 12 equal pieces, we need to first determine the circumference of the pizza.
The formula for the circumference \( C \) of a circle is given by:
\[
C = \pi d
\]
where \( d \) is the diameter. In this case, the diameter \( d \) of the pizza is 24 inches. Thus, the circumference is:
\[
C = \pi \times 24
\]
Calculating the circumference:
\[
C \approx 3.14 \times 24 \approx 75.36 \text{ inches}
\]
Next, when the pizza is cut into 12 equal pieces, we need to determine the total length of the crust along the cuts.
Each cut piece will have a crust edge represented by the cut edges of the pizza. Since the pizza is divided into 12 equal slices, there will be 12 cuts.
The length of each cut edge is equal to the length of the crust on the circumference between cuts, which does not repeat but contributes to the perimeter shared by the slices.
However, each cut does not add additional length to the circumference; they are merely intersecting the crust.
Thus, the total length of the crust that is along these cuts is equal to the circumference. Therefore, the final answer remains:
\[
\text{Total length of the crust along the edges that are cut} = 75.36 \text{ inches}
\]
In conclusion, the total length of the crust along the edges that are cut is approximately ***75.36 inches.***
The formula for the circumference \( C \) of a circle is given by:
\[
C = \pi d
\]
where \( d \) is the diameter. In this case, the diameter \( d \) of the pizza is 24 inches. Thus, the circumference is:
\[
C = \pi \times 24
\]
Calculating the circumference:
\[
C \approx 3.14 \times 24 \approx 75.36 \text{ inches}
\]
Next, when the pizza is cut into 12 equal pieces, we need to determine the total length of the crust along the cuts.
Each cut piece will have a crust edge represented by the cut edges of the pizza. Since the pizza is divided into 12 equal slices, there will be 12 cuts.
The length of each cut edge is equal to the length of the crust on the circumference between cuts, which does not repeat but contributes to the perimeter shared by the slices.
However, each cut does not add additional length to the circumference; they are merely intersecting the crust.
Thus, the total length of the crust that is along these cuts is equal to the circumference. Therefore, the final answer remains:
\[
\text{Total length of the crust along the edges that are cut} = 75.36 \text{ inches}
\]
In conclusion, the total length of the crust along the edges that are cut is approximately ***75.36 inches.***