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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Answer 1

To find the diagonal through the cylinder, which runs from one point on the circular base to the opposite point on the top base, we can use the Pythagorean theorem. The diagonal forms the hypotenuse of a right triangle where one leg is the height of the cylinder and the other leg is the diameter of the circular base.

1. **Calculate the diameter of the circular base:**
\[
\text{Diameter} = 2 \times \text{Radius} = 2 \times 7 = 14 \text{ inches}
\]

2. **Use the Pythagorean theorem to find the diagonal \(d\):**
\[
d = \sqrt{(\text{Diameter})^2 + (\text{Height})^2}
\]
Substituting the values:
\[
d = \sqrt{(14)^2 + (12)^2}
\]
\[
d = \sqrt{196 + 144}
\]
\[
d = \sqrt{340}
\]
\[
d \approx 18.44 \text{ inches}
\]

So the approximate diagonal through the cylinder is **18.44 inches**.