The lateral area of the cone to the nearest whole number is 25,133 m².
To find the lateral area of the cone, we need to use the formula:
Lateral Area = π * r * s
where:
π is pi (approximately 3.14)
r is the radius of the cone's base (half the width)
s is the slant height of the cone
Step 1: Calculate the radius
The radius is half the width of the cone's base, which is:
Radius = Width / 2
Radius = 160 m / 2
Radius = 80 m
Step 2: Calculate the slant height
We can use the Pythagorean theorem to find it. We know the height of the cone (60 m) and the radius (80 m). Slant height forms the hypotenuse of a right triangle with these two sides as legs. Therefore:
Slant height² = Height² + Radius²
Slant height² = 60² m² + 80² m²
Slant height² = 3600 m² + 6400 m²
Slant height² = 10000 m²
Slant height = √10000 m (taking the square root of both sides)
Slant height ≈ 100 m (rounded to the nearest whole number)
Step 3: Calculate the lateral area
Now that we have both the radius and the slant height, we can plug them into the formula:
Lateral Area = π * r * s
Lateral Area ≈ 3.14 * 80 m * 100 m
Lateral Area ≈ 25,133 m² (rounded to the nearest whole number)
Therefore, the lateral area of the cone to the nearest whole number is 25,133 m².