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: Calculate the radius

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

Step2: Apply the Pythagorean theorem

The slant - height $c = 13$ cm. According to the Pythagorean theorem $a^{2}+h^{2}=c^{2}$, where $h$ is the height of the cone. Substitute $a = 4$ and $c = 13$ into the formula: $4^{2}+h^{2}=13^{2}$.

Step3: Solve for $h$

First, calculate $4^{2}=16$ and $13^{2}=169$. The equation becomes $16 + h^{2}=169$. Then, subtract 16 from both sides: $h^{2}=169 - 16=153$. Take the square root of both sides: $h=\sqrt{153}=\sqrt{9\times17}=3\sqrt{17}\approx 12.37$ cm.

Answer:

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