https://file.aiquickdraw.com/mathbot/file/1725312237474imdyoieu.jpg

To calculate the surface area of the cone, we can use the formula for the lateral surface area of a cone:

\[
\text{Surface Area of Cone} = \pi r l
\]

Where:
- \( r \) is the radius of the base of the cone.
- \( l \) is the slant height of the cone.

### Given:
- Radius of the cone \( r = 7 \, \text{cm} \)
- Height of the cone \( h = 13 \, \text{cm} \)

First, we need to find the slant height \( l \) using the Pythagorean theorem:

\[
l = \sqrt{r^2 + h^2}
\]

Let's calculate the slant height \( l \).The slant height \( l \) of the cone is approximately \( 14.76 \, \text{cm} \).

Now, let's calculate the surface area of the cone using the formula:

\[
\text{Surface Area of Cone} = \pi r l
\]

Substituting the values of \( r \) and \( l \).The surface area of the cone is approximately \( 324.70 \, \text{cm}^2 \).

Would you like further details on this calculation or have any other questions?

Here are 5 related questions:
1. How do you calculate the total surface area of the solid, including the hemisphere?
2. What is the volume of the cone?
3. How does the radius affect the surface area of the cone?
4. What is the surface area of the hemisphere in the diagram?
5. Can you explain the Pythagorean theorem used in this context?

**Tip:** Always verify your units when calculating areas, volumes, or other measurements to avoid errors.

Learn how to calculate the surface area of a cone using the formula for the lateral surface area and the Pythagorean theorem. Given a cone with radius 7 cm and height 13 cm, find the slant height and surface area. Detailed step-by-step solution with mathematical concepts and formulas.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation