Question

find h. first we must set up our equation using the pythagorean theorem. a² + b² = c² 13 cm ?² + b² = ² hint: plug in the value of the cones radius for a. the diameter of the cone is 8. the radius is half this value.

Explanation:

Step1: Find the radius

The diameter of the cone is 8 cm. The radius $r$ is half of the diameter, so $r=\frac{8}{2}=4$ cm.

Step2: Apply the Pythagorean theorem

For a cone, if the slant - height is $l = 13$ cm, the radius is $r$ and the height is $h$, by the Pythagorean theorem $r^{2}+h^{2}=l^{2}$. Substituting $r = 4$ cm and $l = 13$ cm into the formula, we get $4^{2}+h^{2}=13^{2}$. Then $h^{2}=13^{2}-4^{2}$.

Step3: Calculate $h^{2}$

$13^{2}=169$ and $4^{2}=16$. So $h^{2}=169 - 16=153$.

Step4: Find $h$

$h=\sqrt{153}=\sqrt{9\times17}=3\sqrt{17}\approx 12.37$ cm.

Answer:

$h = 3\sqrt{17}\text{ cm}\approx12.37$ cm