Bot GPT 4-o mini To find the height \( h \) of the cylinder using the given radius \( r \) and diagonal \( d \), we can use the Pythagorean theorem. In this case, the radius forms one leg of a right triangle, the height \( h \) is the other leg, and the diagonal \( d \) is the hypotenuse.
According to the Pythagorean theorem: \[ d^2 = r^2 + h^2 \]
Here, we have:
- \( r = 5 \) cm
- \( d = 15 \) cm
Substituting these values into the equation, we get: \[ 15^2 = 5^2 + h^2 \] \[ 225 = 25 + h^2 \] \[ 225 - 25 = h^2 \] \[ 200 = h^2 \] \[ h = \sqrt{200} \] \[ h \approx 14.14 \]
Rounding \( h \) to the nearest tenth gives us: \[ h \approx 14.1 \text{ cm} \]
Thus, the answer is:
14.1 cm
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