Question

The radius of a right cone is 8 inches. The slant height of the cone is 10 inches.

Use the Pythagorean theorem to find the height of the cone.

Step 1: Identify the legs and hypotenuse of the right triangle.

A = *blank 1*

B = *blank 2*

C = *blank 3*

Answer 1

To find the height of the cone using the Pythagorean theorem, we can identify the legs and the hypotenuse of the right triangle formed by the radius, height, and slant height of the cone.

In this case:

- A = the height of the cone (the unknown we're trying to find)
- B = the radius of the cone, which is 8 inches
- C = the slant height of the cone, which is 10 inches

So we can fill in the blanks as follows:

A = height of the cone

B = 8 inches (radius)

C = 10 inches (slant height)

Now you can apply the Pythagorean theorem, which states that:

\[
A^2 + B^2 = C^2
\]

Substituting in the known values:

\[
A^2 + 8^2 = 10^2
\]

From here, you can solve for the height \( A \).