A CCTV camera has installed on the top of a straight pole of 8meter height such that forward traffic can be seen from the line of sight of 10meters . Find the area of circular path formed by shadow around the pole.(π=3.14)
Answers
Solution:
[See the figure attached]
Height of Straight Pole, OY = 8 m
Distance from which forward traffic can be seen from the line of sight, XY = 10m
Radius of the circular path formed by the shadow around the pole, OX = ?
In the triangle XOY let us apply Pythagoras Theorem to find OX,
Perpendicular² + Base² = Hypotenuse²
OA² + OX² = XY²
8² + OX² = 10²
OX² = 10² - 8²
OX² = 100 - 64
OX² = 36
OX = √36
OX = 6
The radius of the circular path formed by the shadow around the pole is OX i.e. 6 m.
Now, we have to find out the area of the circular path formed by shadow around the pole.
Area of circle = π r²
whereas,
π = 3.14
r = OX = 6 m
Area of circular path = π r² = 3.14 * 6² = 3.14 * 36 = 113.04 m²
The area of circular path formed by shadow around the pole is 113.04 m²
