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*

Step 2 substitute values into the Pythagoreon therom a² + b² = c²

Step 3 solve the equation to find the missing length

Answer 1

To find the height of the right cone using the Pythagorean theorem, we need to identify the parts of the right triangle formed by the radius, height, and slant height of the cone.

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

- A = height of the cone (h)
- B = radius of the cone (r)
- C = slant height of the cone (l)

Given:
- r = 8 inches
- l = 10 inches

Now we can fill in the blanks:

A = height (h) = *blank 1*
B = radius (r) = 8 inches (this goes in *blank 2*)
C = slant height (l) = 10 inches (this goes in *blank 3*)

### Step 2: Substitute values into the Pythagorean theorem \( a^2 + b^2 = c^2 \)

Here, we can write it as:
- \( h^2 + r^2 = l^2 \)

Substituting the known values:
- \( h^2 + (8)^2 = (10)^2 \)

### Step 3: Solve the equation to find the missing length

Now, plug in the values and solve for \( h \):
- \( h^2 + 64 = 100 \) (since \( 8^2 = 64 \) and \( 10^2 = 100 \))

Now, isolate \( h^2 \):
- \( h^2 = 100 - 64 \)
- \( h^2 = 36 \)

Taking the square root of both sides to find \( h \):
- \( h = \sqrt{36} \)
- \( h = 6 \) inches

### Conclusion
The height of the cone is 6 inches.