To find the slant height of the cone using the Pythagorean theorem, we can use the relationship between the radius, height, and slant height of the cone.
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Determine the radius:
- The diameter of the cone is 13 cm, so the radius \( r \) is: \[ r = \frac{d}{2} = \frac{13 , \text{cm}}{2} = 6.5 , \text{cm} \]
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Given the height:
- The height \( h \) of the cone is given as 6 cm.
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Using the Pythagorean Theorem:
- The slant height \( L \) of the cone, the height \( h \), and the radius \( r \) form a right triangle, where: \[ L^2 = h^2 + r^2 \]
- Substituting the values: \[ L^2 = 6^2 + (6.5)^2 \] \[ L^2 = 36 + 42.25 \] \[ L^2 = 78.25 \] \[ L = \sqrt{78.25} \approx 8.8 , \text{cm} \]
Thus, the slant height of the cone is approximately 8.8 cm.
The correct response is:
- 8.8 cm