A sensor light installed on the edge of a home can detect motion for a distance of 63ft in front?

Question

and with a range of motion of 225 degrees Over what area will the sensor detect motion and become illuminated?

Answer 1

If the range of motion were 360 degrees, the light would illuminate a circle with radius 63 ft.

Area of that circle = pi * 63^2 = 12462.7 square feet

225 degrees is 225/360 of the whole circle.

225/360 = x/12462.7
x = 7789.2 square feet

Answer 2

Let's consider the range as a circle with radius of 63 feet. Let's find the area of that circle:

A = pi(r^2)
A = pi(63^2)
A = 12,469 ft^2

Now, it can only see 225 degrees of the circle. That is 225/360 for a whole circle. Let's multiply:

12,469 * 225/360 = 7,793 ft^2

Answer 3

Radius: 225
Height: 63

Slant Height: 233.653589743
Lateral (not including base) Surface Area: 165159.99023
Total Surface Area: 324203.118318