Final answer:
The lateral area of the traffic cone is approximately 932 square inches.
Step-by-step explanation:
To find the lateral area of a traffic cone, we need to calculate the area of the curved surface that makes up the cone. The lateral area is given by the formula:
Lateral Area = πr×l
where r is the radius of the base of the cone and l is the slant height. The slant height can be found using the Pythagorean theorem: l² = r² + h², where h is the height of the cone.
In this case, the radius is 10 inches and the height is 28 inches. Plugging in these values, we can calculate the slant height and then find the lateral area.
Lateral Area = π × 10 × √(10² + 28²)
Lateral Area ≈ 3.14 × 10 × 29.7 ≈ 932.2 square inches
Rounded to the nearest whole number, the lateral area of the traffic cone is 932 square inches.