Question

A cctv camera is placed on the top of a 24m high pole in such a way that traffic can be beyond 25m of the line of sight of it. Find the area of the green path around the pole

Answer 1

The Area of the green path around the pole is 153.86 sq meters

Step-by-step explanation:

Given as :

The height of pole = h = 24 meters

A CCTV camera is placed on the top of pole

The camera can see at distance straight line from the top = d = 25 meters

Let The Area of the green path around the pole = A sq meters

Let The radius surrounding the pole = r m

According to question

Using Pythagoras Theorem

radius² + height² = distance²

i.e r² + h² = d²

Or,  r² + (24 m) ² = (25 m) ²

Or,  r² = (25 m) ² - (24 m) ²

Or,  r² = 625 - 576

∴     r² = 49

i.e  r = √49

Or, radius = r = 7  meters

Again

Area of the green path around the pole = π × radius²  sq meters

Or,                                                            A = 3.14 × 7²

Or,                                                            A = 3.14 × 49

∴                                                               A = 153.86 m²

So, The Area of the green path around the pole = A = 153.86 m²

Hence, The Area of the green path around the pole is 153.86 sq meters Answer

Answer 2

Answer:

153.86 m²

Step-by-step explanation:

height of pole = h= 24 m

___________= d = 25 m

let ,

area of green patch around pole = A m²

radius = R m

according to question ,

Using pythagoras theorem ,

H² = B² + P²

B² = H² - P²

B² = (25)² - (24)²

B² = 625 - 576

B² = 49

$B = \sqrt{49}$

B = 7 m

area around pole =

$\pi r²$

= 3.14 × 7 × 7

= 3.14 × 49

= 153.86 m²