Question
Find the slant height of the square pyramid. Round to the nearest whole inch, if necessary. .....(12 in and 18 in) Which of these is the answer A:8 in...B:15 in....C:6 in...D:13 in....
Answers
GPT-4o mini
To find the slant height of a square pyramid, we can use the Pythagorean theorem. In a square pyramid, the slant height (\(l\)) can be found using the formula:
\[
l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2}
\]
where:
- \(h\) is the height of the pyramid,
- \(b\) is the length of a side of the base square.
Given:
- Height (\(h\)) = 18 inches,
- Base side length (\(b\)) = 12 inches.
First, we need to calculate \(\frac{b}{2}\):
\[
\frac{b}{2} = \frac{12}{2} = 6 \text{ in}
\]
Now we can plug the values into the slant height formula:
\[
l = \sqrt{18^2 + 6^2}
\]
\[
l = \sqrt{324 + 36}
\]
\[
l = \sqrt{360}
\]
Calculating \(\sqrt{360}\):
\[
\sqrt{360} \approx 18.97
\]
Rounding to the nearest whole inch, we get:
\[
l \approx 19 \text{ in}
\]
Since none of the provided answer choices (A: 8 in, B: 15 in, C: 6 in, D: 13 in) is 19 inches, it appears there might be a misunderstanding in the provided answer options or the problem context. Please double-check the values or options given.
\[
l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2}
\]
where:
- \(h\) is the height of the pyramid,
- \(b\) is the length of a side of the base square.
Given:
- Height (\(h\)) = 18 inches,
- Base side length (\(b\)) = 12 inches.
First, we need to calculate \(\frac{b}{2}\):
\[
\frac{b}{2} = \frac{12}{2} = 6 \text{ in}
\]
Now we can plug the values into the slant height formula:
\[
l = \sqrt{18^2 + 6^2}
\]
\[
l = \sqrt{324 + 36}
\]
\[
l = \sqrt{360}
\]
Calculating \(\sqrt{360}\):
\[
\sqrt{360} \approx 18.97
\]
Rounding to the nearest whole inch, we get:
\[
l \approx 19 \text{ in}
\]
Since none of the provided answer choices (A: 8 in, B: 15 in, C: 6 in, D: 13 in) is 19 inches, it appears there might be a misunderstanding in the provided answer options or the problem context. Please double-check the values or options given.