Question

surface area of a cone
diameter=25
slant height=22

Answer 1

To find the surface area of a cone, you can use the following formula:

\[
\text{Surface Area} = \pi r (r + l)
\]

where:
- \( r \) is the radius of the base,
- \( l \) is the slant height.

Given:
- The diameter of the cone is 25, so the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{25}{2} = 12.5
\]

- The slant height \( l \) is given as 22.

Now, plug these values into the surface area formula:

\[
\text{Surface Area} = \pi (12.5) (12.5 + 22)
\]

Calculating the inside of the parentheses:

\[
12.5 + 22 = 34.5
\]

Now substitute this back into the formula:

\[
\text{Surface Area} = \pi (12.5) (34.5)
\]

Now calculate \( 12.5 \times 34.5 \):

\[
12.5 \times 34.5 = 431.25
\]

Finally multiply by \( \pi \):

\[
\text{Surface Area} \approx 431.25 \times 3.14159 \approx 1355.45
\]

Thus, the surface area of the cone is approximately \( 1355.45 \) square units.