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?

Question

(4 points)
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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.