Bot GPT 4-o mini To find the height \( h \) of the cylinder using the radius \( r \) and the diagonal \( d \), we can use the Pythagorean theorem. The diagonal of the cylinder (in this context) forms a right triangle with the height and the radius.
The relationship can be expressed as:
\[ d^2 = h^2 + r^2 \]
Given:
- The radius \( r = 5 \) cm
- The diagonal \( d = 15 \) cm
Substituting the values into the equation:
\[ 15^2 = h^2 + 5^2 \]
Calculating the squares:
\[ 225 = h^2 + 25 \]
Now, subtract 25 from both sides:
\[ 225 - 25 = h^2 \]
\[ 200 = h^2 \]
Take the square root of both sides to find \( h \):
\[ h = \sqrt{200} \]
Calculating \( \sqrt{200} \):
\[ h \approx 14.14 \]
Rounding this to the nearest tenth gives:
\[ h \approx 14.1 , \text{cm} \]
So the correct answer for the height \( h \) of the cylinder is approximately 14.1 cm.
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