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

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 2

thats totally wrong-

Answer 3

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 4

thank you and you sure thats correct just wanna make sure

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!