Question

A right cone has a slant height of 17 feet, and the diameter of the base is 30 feet. What is the height, h, of the cone?
An image displaying a right cone that has a slant height of 17 feet, and the diameter of the base is 30 feet. What is the height, h, of the cone?
A.
64 ft
B.
13 ft
C.
D.
8 ft

Answer 1

To find the height \( h \) of the right cone, we can use the relationship between the slant height \( l \), the radius \( r \), and the height \( h \) of the cone, which can be described by the Pythagorean theorem:

\[
l^2 = r^2 + h^2
\]

Given:
- The slant height \( l = 17 \) feet
- The diameter of the base is \( 30 \) feet, which means the radius \( r = \frac{30}{2} = 15 \) feet

Now, substituting the known values into the Pythagorean theorem:

\[
17^2 = 15^2 + h^2
\]

Calculating the squares:

\[
289 = 225 + h^2
\]

Now, solving for \( h^2 \):

\[
h^2 = 289 - 225
\]
\[
h^2 = 64
\]

Taking the square root of both sides:

\[
h = \sqrt{64} = 8 \text{ feet}
\]

Thus, the height \( h \) of the cone is \( \boxed{8} \) ft.