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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?

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Answers :
Double the radius to get the diameter = 14 in
Use phythagorean theorem with the height 12 in and the diameter 14 in - 12^2 + 14^2 = d^2
Simply to get: d^2 = 340
Answer - d = 18.4
Use the pythagorean theorem with the height 12 in and the radius 7 in - 12^2 + 7^2 = d^2
Simply 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 12 in and the diameter 49 in - 12^2 + 49^2 = d^2
Simplify the equation to get: d^2 = 2545
Answer - d = 50.4

1 answer

To find the approximate diagonal through the cylinder, we need to 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 cylinder.

Here are the steps:

  1. Calculate the diameter of the cylinder: The diameter (d) is twice the radius (r). So, if the radius is 7 inches, the diameter is: \[ d = 2 \times 7 = 14 \text{ inches} \]

  2. Use the Pythagorean theorem: Now, we apply the theorem with the height (h = 12 inches) and the diameter (which we just calculated as 14 inches): \[ \text{diagonal}^2 = \text{height}^2 + \text{diameter}^2 \] \[ \text{diagonal}^2 = 12^2 + 14^2 \] \[ \text{diagonal}^2 = 144 + 196 = 340 \]

  3. Calculate the diagonal: Now take the square root of 340 to find the diagonal: \[ \text{diagonal} = \sqrt{340} \approx 18.44 \text{ inches} \]

Rounded to one decimal place, the answer is approximately 18.4 inches.

The correct selection based on the responses provided would be:

  • "Double the radius to get the diameter = 14 in"
  • "Use Pythagorean theorem with the height 12 in and the diameter 14 in - 12^2 + 14^2 = d^2"
  • "Simplify to get: d^2 = 340"
  • "Answer - d = 18.4"