Question

A spyglass in the shape of a cone has a slant height of 18 cm and a radius of 6 cm what is the surface area of the spylass use 3.14 as pi

Answer 1

thats totally wrong-

Answer 2

thank you and you sure thats correct just wanna make sure

Answer 3

To find the surface area of a cone, you can use the formula:

\[
\text{Surface Area} = \pi r (r + l)
\]

where:
- \( r \) is the radius of the base,
- \( l \) is the slant height.

In this case:
- \( r = 6 \) cm,
- \( l = 18 \) cm,
- \( \pi \) is given as 3.14.

Now, substituting the values into the formula:

1. Calculate the lateral surface area:

\[
\text{Lateral Surface Area} = \pi r l = 3.14 \times 6 \times 18
\]

Calculating this:

\[
= 3.14 \times 6 = 18.84
\]
\[
= 18.84 \times 18 = 338.88 \text{ cm}^2
\]

2. Calculate the base area:

\[
\text{Base Area} = \pi r^2 = 3.14 \times (6)^2 = 3.14 \times 36
\]

Calculating this:

\[
= 3.14 \times 36 = 113.04 \text{ cm}^2
\]

3. Finally, add the lateral surface area and the base area to find the total surface area:

\[
\text{Total Surface Area} = \text{Lateral Surface Area} + \text{Base Area} = 338.88 + 113.04 = 451.92 \text{ cm}^2
\]

Thus, the surface area of the spyglass is approximately:

\[
\text{Surface Area} \approx 451.92 \text{ cm}^2
\]

Answer 4

I apologize for any confusion! Let's go through the calculations again step by step to ensure we get the correct surface area of the cone-shaped spyglass.

The formula for the surface area of a cone is:

\[
\text{Surface Area} = \pi r (r + l)
\]

where:
- \( r \) = radius of the base,
- \( l \) = slant height.

Given:
- \( r = 6 \) cm,
- \( l = 18 \) cm,
- \( \pi = 3.14 \).

### Step 1: Calculate the lateral surface area

\[
\text{Lateral Surface Area} = \pi r l = 3.14 \times 6 \times 18
\]

Calculating this:

1. Calculate \( 6 \times 18 \):
\[
6 \times 18 = 108
\]

2. Then multiply by \( \pi \):
\[
3.14 \times 108 = 339.12 \text{ cm}^2
\]

### Step 2: Calculate the base area

\[
\text{Base Area} = \pi r^2 = 3.14 \times (6^2) = 3.14 \times 36
\]

Calculating this:

\[
3.14 \times 36 = 113.04 \text{ cm}^2
\]

### Step 3: Total surface area

Now, add the lateral surface area and the base area together:

\[
\text{Total Surface Area} = \text{Lateral Surface Area} + \text{Base Area}
\]

\[
= 339.12 + 113.04 = 452.16 \text{ cm}^2
\]

So, the correct surface area of the spyglass is approximately:

\[
\text{Surface Area} \approx 452.16 \text{ cm}^2
\]

Thank you for your patience, and I hope this clears up any confusion!

Answer 5

Yes, let's carefully verify the calculations one more time to ensure everything is correct:

### Given values:
- Radius \( r = 6 \) cm
- Slant height \( l = 18 \) cm
- \( \pi \approx 3.14 \)

### Step 1: Calculate the lateral surface area

The formula for the lateral surface area of a cone is:

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

Substituting the values:

\[
\text{Lateral Surface Area} = 3.14 \times 6 \times 18
\]

Calculating this step-by-step:

1. Calculate \( 6 \times 18 = 108 \).
2. Then multiply by \( 3.14 \):
\[
3.14 \times 108 = 339.12 \text{ cm}^2
\]

### Step 2: Calculate the base area

The formula for the base area of a cone is:

\[
\text{Base Area} = \pi r^2
\]

Substituting the values:

\[
\text{Base Area} = 3.14 \times (6^2) = 3.14 \times 36
\]

Calculating this:

\[
3.14 \times 36 = 113.04 \text{ cm}^2
\]

### Step 3: Total surface area

Now we add the lateral surface area and the base area:

\[
\text{Total Surface Area} = \text{Lateral Surface Area} + \text{Base Area}
\]
\[
\text{Total Surface Area} = 339.12 + 113.04 = 452.16 \text{ cm}^2
\]

### Conclusion

Thus, the total surface area of the spyglass is:

\[
\text{Surface Area} \approx 452.16 \text{ cm}^2
\]

These calculations have been thoroughly verified, and the answer provided is indeed correct. Thank you for your patience, and if you have any additional questions, feel free to ask!