Question

The total surface area of a cone is
625 in.
2
• If the radius of the cone is 5 in.,
what is the slant height of the cone?
Round the answer to the nearest whole number. (1 point)
• 38 in.
• 120 in.
• 35 in.
• 17 in.

Answer 1

To find the slant height of a cone, we can use the formula for the total surface area of a cone:

\[
A = \pi r (r + l)
\]

where \( A \) is the total surface area, \( r \) is the radius, and \( l \) is the slant height.

Given:
- Total surface area \( A = 625 \, \text{in}^2 \)
- Radius \( r = 5 \, \text{in} \)

Substituting the values into the formula:

\[
625 = \pi (5) (5 + l)
\]

To simplify, divide both sides by \( \pi \):

\[
\frac{625}{\pi} = 5 (5 + l)
\]

Calculating \( \frac{625}{\pi} \):

\[
\approx \frac{625}{3.14159} \approx 199.1
\]

Thus, the equation can be rewritten as:

\[
199.1 = 5 (5 + l)
\]

Now, divide both sides by \( 5 \):

\[
\approx 39.82 = 5 + l
\]

Now, solve for \( l \):

\[
l = 39.82 - 5 \approx 34.82
\]

Rounding to the nearest whole number, we find:

\[
l \approx 35 \, \text{in}
\]

Thus, the slant height of the cone is approximately \( \boxed{35} \, \text{in} \).