What is the surface area, in square inches, of a cone with a radius of 10 inches and a slant height of 15 inches? Use 3.14 for pi.(1 point)

Responses

471 square inches
471 square inches
1,177.5 square inches
1,177.5 square inches
2,198 square inches
2,198 square inches
785 square inches

1 answer

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

\[ \text{Surface Area} = \pi r^2 + \pi r l \]

where:

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

In this case, the radius \( r = 10 \) inches and the slant height \( l = 15 \) inches.

  1. Calculate the base area (circular area): \[ \pi r^2 = 3.14 \times (10^2) = 3.14 \times 100 = 314 \text{ square inches} \]

  2. Calculate the lateral surface area (the area of the cone's side): \[ \pi r l = 3.14 \times 10 \times 15 = 3.14 \times 150 = 471 \text{ square inches} \]

  3. Add the two areas together to find the total surface area: \[ \text{Surface Area} = 314 + 471 = 785 \text{ square inches} \]

Thus, the total surface area of the cone is 785 square inches.