To find the slant height of the cone, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle, where the other two sides are the height of the cone and the radius of the base.
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Calculate the radius from the diameter: \[ \text{Diameter} = 13 \text{ cm} \] \[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{13 \text{ cm}}{2} = 6.5 \text{ cm} \]
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Use the height of the cone, which is given as: \[ \text{Height} = 6 \text{ cm} \]
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Now apply the Pythagorean theorem \(a^2 + b^2 = c^2\): \[ r^2 + h^2 = l^2 \] where \(r\) is the radius, \(h\) is the height, and \(l\) is the slant height.
Plugging in the values: \[ (6.5)^2 + (6)^2 = l^2 \] \[ 42.25 + 36 = l^2 \] \[ 78.25 = l^2 \]
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To find \(l\), take the square root: \[ l = \sqrt{78.25} \approx 8.8 \text{ cm} \]
Thus, the slant height must be approximately 8.8 cm.
The correct response is: 8.8 cm.
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