A spyglass in the shape of a cone has a slant height of 18 centimeters and a radius of 6 centimeters. What is the surface area of the spyglass? Use 3.14 for pi.(1 point)

Question

Responses

1,356.48 square centimeters
1,356.48 square centimeters

452.16 square centimeters
452.16 square centimeters

197.82 square centimeters
197.82 square centimeters

339.12 square centimeters

Answer 1

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

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

where:

• \( r \) is the radius of the base,
• \( l \) is the slant height.

Given:

• Radius \( r = 6 \) centimeters,
• Slant height \( l = 18 \) centimeters,
• Use \( \pi = 3.14 \).

Now, plug in the values into the surface area formula:

\[ \text{Surface Area} = 3.14 \times 6 \times (6 + 18) \]

First, calculate \( 6 + 18 \):

\[ 6 + 18 = 24 \]

Now, substitute that back into the equation:

\[ \text{Surface Area} = 3.14 \times 6 \times 24 \]

Next, calculate \( 3.14 \times 6 \):

\[ 3.14 \times 6 = 18.84 \]

Now multiply that by 24:

\[ 18.84 \times 24 = 452.16 \]

Thus, the surface area of the spyglass is:

\[ \text{Surface Area} = 452.16 \text{ square centimeters} \]

The correct response is:

452.16 square centimeters