A cellphone tower with signals reaching up to 500 m is set up on a conical hill of height 1.5 km and base radius 2 km. Assuming the tower’s height to be negligible compared to the hill, the area served by the tower (in km²) is (area of curved surface of a right circular cone = π × base radius × slant height):

Correct option is A

Solution:
The signal reaches 500 m = 0.5 km along the surface of the hill.
First, find the slant height of the full hill.
Slant height = √(height² + radius²) = √(1.5² + 2²) = √(2.25 + 4) = √6.25 = 2.5 km
Now, the tower covers only the top portion of the hill with slant height 0.5 km.
By similarity of cones:
Radius of the smaller cone = (0.5 / 2.5) × 2 = (1/5) × 2 = 0.4 km
Area served (curved surface of smaller cone):
Area = π × base radius × slant height = π × 0.4 × 0.5 = 0.2π km²
Correct answer:
(a) 0.2π