What are the lateral area and the surface area of the cone shown below? Round the answers to the nearest tenth. The figure is not drawn to scale.
a cone 14 27
(1 point)
To calculate the lateral area of a cone, you can use the formula:
Lateral area = πrs
Where r is the radius of the cone's base and s is the slant height of the cone.
Given that the radius of the cone is 14 and the slant height is 27, the lateral area can be calculated as:
Lateral area = π(14)(27) ≈ 1193.0 square units
To calculate the surface area of the cone, you can use the formula:
Surface area = πr(r + s)
Given the same values for radius and slant height, the surface area can be calculated as:
Surface area = π(14)(14 + 27) ≈ 1087.4 square units
Therefore, the lateral area of the cone is approximately 1193.0 square units and the surface area is approximately 1087.4 square units.