https://file.aiquickdraw.com/mathbot/file/1729620556140wpvasw6n.jpg

To solve this problem, we need to calculate the **total surface area** of the cone, which includes both the curved surface area and the area of the base.

### 1. **Curved Surface Area**  
The formula for the curved surface area of a cone is given as:  
\[
A_{\text{curved}} = \pi r l
\]
Where:
- \( r = 8 \, \text{m} \) (the radius)
- \( l = 21 \, \text{m} \) (the slant height)

Substitute these values into the formula:
\[
A_{\text{curved}} = \pi \times 8 \times 21 = 168 \pi
\]
Now, approximate using \( \pi \approx 3.1416 \):
\[
A_{\text{curved}} \approx 168 \times 3.1416 = 527.79 \, \text{m}^2
\]

### 2. **Area of the Base**  
The base of the cone is a circle, and the area of a circle is given by:
\[
A_{\text{base}} = \pi r^2
\]
Substitute \( r = 8 \, \text{m} \) into the formula:
\[
A_{\text{base}} = \pi \times 8^2 = 64 \pi
\]
Now, approximate:
\[
A_{\text{base}} \approx 64 \times 3.1416 = 201.06 \, \text{m}^2
\]

### 3. **Total Surface Area**  
The total surface area is the sum of the curved surface area and the area of the base:
\[
A_{\text{total}} = A_{\text{curved}} + A_{\text{base}} = 527.79 + 201.06 = 728.85 \, \text{m}^2
\]

### Final Answer:
The total surface area of the cone is approximately **728.9 m²** (to 1 decimal place).

---

Would you like a more detailed explanation of any step or have any questions? Here are five related questions you could explore:

1. How would the total surface area change if the slant height increased?
2. Can you derive the formula for the volume of a cone?
3. What is the surface area if the radius was doubled?
4. How do you calculate the lateral surface area for a frustum of a cone?
5. How does the surface area of a sphere compare to that of a cone with the same radius?

**Tip**: Always double-check whether the slant height or the perpendicular height is provided in cone problems.

Work out the total surface area of the cone shown below. Give your answer to 1 decimal place.

Learn how to find the total surface area of a cone with a radius of 8 meters and a slant height of 21 meters. The solution uses key formulas, including the curved surface area and area of a circle, providing a final answer of 728.9 m² rounded to 1 decimal place.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation