a cone has sa 128.93msquared and radius 3.6m what is the slant heigh to the nearest tenth

The surface area \( A \) of a cone is given by the formula:

\[
A = \pi r l + \pi r^2
\]

Where:
- \( A \) is the surface area (128.93 m²),
- \( r \) is the radius (3.6 m),
- \( l \) is the slant height (which we are trying to find).

First, let's plug in the known values into the formula:

\[
128.93 = \pi \cdot 3.6 \cdot l + \pi \cdot (3.6)^2
\]

We can now solve for \( l \). Let me calculate that for you.The slant height of the cone is approximately \( 7.8 \) meters to the nearest tenth.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:
1. How is the lateral surface area of a cone calculated?
2. How does the formula for the volume of a cone differ from the surface area formula?
3. What happens to the slant height if the radius is doubled?
4. How would the surface area change if the slant height increased by 10%?
5. Can you calculate the height of the cone given the slant height and radius?

**Tip:** The slant height connects the radius and the height of the cone via the Pythagorean theorem.

A cone has a surface area of 128.93 m² and a radius of 3.6 m. What is the slant height to the nearest tenth?

Discover how to calculate the slant height of a cone with a surface area of 128.93 m² and a radius of 3.6 m. This problem involves using the surface area formula of a cone and algebraic manipulation, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation