https://file.aiquickdraw.com/mathbot/file/1730118705519pzqeuzds.jpg

To solve this problem, we need to find the **lateral surface area** and the **total surface area** of a cone with the following details:

- **Slant height** (\( l \)) = 7 ft
- **Diameter of the base** = 8 ft, which gives a **radius** (\( r \)) = 4 ft
- **Value of \( \pi \)** = 3.14 (as specified)

### Step 1: Lateral Surface Area
The formula for the lateral surface area (\(A_{lateral}\)) of a cone is:
\[
A_{lateral} = \pi \times r \times l
\]
Substitute the values:
\[
A_{lateral} = 3.14 \times 4 \times 7 = 87.92 \text{ ft}^2
\]

### Step 2: Total Surface Area
The total surface area (\(A_{total}\)) of a cone includes both the lateral surface area and the area of the base. The formula for the total surface area is:
\[
A_{total} = A_{lateral} + A_{base}
\]
where the base area \(A_{base}\) is given by:
\[
A_{base} = \pi \times r^2
\]
Calculate the base area:
\[
A_{base} = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \text{ ft}^2
\]

Now, add the lateral surface area and the base area to get the total surface area:
\[
A_{total} = 87.92 + 50.24 = 138.16 \text{ ft}^2
\]

### Final Answers
- **Lateral Surface Area**: 87.92 ft²
- **Total Surface Area**: 138.16 ft²

Would you like further clarification on any part of the solution?

---

Here are 5 related questions to expand your understanding:

1. How would the surface areas change if the diameter were doubled?
2. How can you calculate the volume of this cone?
3. What if the cone had a different slant height but the same radius?
4. How does the use of a more precise value for \( \pi \) (e.g., 3.14159) affect the surface area?
5. What is the difference between lateral and total surface area for a cone?

**Tip:** For cones, the radius is half the diameter, which is essential for calculations involving circles.

Find the lateral surface area and surface area of a cone with a slant height of 7 ft and a base diameter of 8 ft. Use 3.14 for π.

Learn how to calculate the lateral and total surface area of a cone with a 7 ft slant height and 8 ft diameter. This problem covers key geometry concepts, including the use of π (3.14) and essential cone surface area formulas. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation