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)
2,198 square inches
2,198 square inches
785 square inches
785 square inches
1,177.5 square inches
1,177.5 square inches
471 square inches
To find the surface area of a cone, you need to calculate both the base area and the lateral (side) surface area. The base is a circle with the formula for its area as \( A_{base} = \pi r^2 \), where r is the radius of the base. The lateral surface area of a cone is given by the formula \( A_{lateral} = \pi r l \), where l is the slant height of the cone.
Given:
- The radius \( r = 10 \) inches
- The slant height \( l = 15 \) inches
- Use \( \pi \approx 3.14 \)
Now calculate both areas:
\( A_{base} = \pi r^2 = 3.14 \times 10^2 = 3.14 \times 100 = 314 \) square inches
\( A_{lateral} = \pi r l = 3.14 \times 10 \times 15 = 3.14 \times 150 = 471 \) square inches
Now add both areas to find the total surface area of the cone:
\( A_{total} = A_{base} + A_{lateral} = 314 + 471 = 785 \) square inches
So, the correct answer is:
785 square inches