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? explain in 4 steps

Answer 1

1. Calculate the length of the diagonal of the right triangle formed by the radius (7 inches), the height (12 inches), and the diagonal of the cylinder.

2. Use the Pythagorean theorem to find the length of the diagonal. The Pythagorean theorem states that the square of the length of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides.

3. In this case, the length of the hypotenuse (diagonal) is unknown, the length of one of the sides is the radius (7 inches), and the length of the other side is the height (12 inches). Plug these values into the Pythagorean theorem equation:

(diagonal)^2 = (radius)^2 + (height)^2
(diagonal)^2 = 7^2 + 12^2
(diagonal)^2 = 49 + 144
(diagonal)^2 = 193

4. Calculate the square root of 193 to find the actual length of the diagonal:
diagonal ≈ √193
diagonal ≈ 13.89 inches

Therefore, the approximate length of the diagonal through the cylinder would be 13.89 inches.