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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Step 1
Step 2
Step 3
Step 4 - answer

Responces:
Double the radius to get the diameter = 14 in.
Use Pythagorean Theorem with the hieght 122 in and the diameter 14 in - 112^(2) + 14^(2) = d^(2).
Simplify to get: d^(2) = 340.
Answer - d ~ 18.4
Use the Pythagorean Theorem with the hieght 12 in and the radius 7 in - 12^(2) + 7^(2) = d^(2).
Simplify to get: d^(2) = 193.
Answer - d = 96.5
Answer - d = 170
Square the radius to get the diameter = 49 in.
Use Pythagorean Theorem with the height 12in and the diameter 49 in - 12^(2) + 49^(2) = d^(2).
Ssimplify the equation to get: d^(2) = 2,545.
Answer - d ~ 50.4

Answer 1

To find the diagonal through the cylinder, we will use the Pythagorean Theorem. Here, we need to consider the height and the diameter of the cylinder.

1. The radius of the cylinder is given as 7 inches. Therefore, the diameter \(D\) is calculated as: \[ D = 2 \times \text{radius} = 2 \times 7 = 14 \text{ inches} \]

2. Now we will use the Pythagorean Theorem to find the diagonal \(d\). The height \(h\) is given as 12 inches, and we will treat the diameter as the base: \[ d^{2} = h^{2} + D^{2} \] \[ d^{2} = 12^{2} + 14^{2} \] \[ d^{2} = 144 + 196 = 340 \]

3. Solving for \(d\): \[ d = \sqrt{340} \approx 18.4 \text{ inches} \]

So the final answer is approximately: Answer - d ~ 18.4