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 is 8 cm, so the radius $a=\frac{8}{2}=4$ cm.

Step2: Apply the Pythagorean - Theorem

The slant height $c = 13$ cm. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $b = h$ (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 $13^{2}=169$. Then the equation becomes $16 + h^{2}=169$. 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:

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