Question

What would the approximate diagonal through the cylinder be in inches if the radius of the cylinder is 7 inches and the height of the cylinder is 12 inches?

(4 points)
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Step 4 - answer

Answer 1

To calculate the approximate diagonal through the cylinder, we can use the Pythagorean theorem in three dimensions. The diagonal \(d\) can be found using the formula:

\[
d = \sqrt{h^2 + (2r)^2}
\]

where:
- \(h\) is the height of the cylinder,
- \(r\) is the radius of the cylinder.

Given:
- Height \(h = 12\) inches,
- Radius \(r = 7\) inches.

Now we can input these values into the formula:

\[
d = \sqrt{12^2 + (2 \times 7)^2}
\]
\[
d = \sqrt{12^2 + 14^2}
\]
\[
d = \sqrt{144 + 196}
\]
\[
d = \sqrt{340}
\]
\[
d \approx 18.44 \text{ inches}
\]

Therefore, the approximate diagonal through the cylinder is **18.44 inches**.