Question

A straight and 15 meter high pole has CCTV camera for traffic control. Which can see traffic from the top of the pole up to 113m of sight line. This camera can see how much traffic around the pole.

Answer 1

Answer:

The CCTV covers 39242 m² of area.

Step-by-step explanation:

Given :

Height of the pole = 15 m

The camera can see = up to 113 m

To find :

Area till it can see traffic

Solution :

The area under the CCTV's surveillance would be a circle. The value of radius needs to be found. Radius of the circle formed will be the base of the triangle formed.

★ By Pythagoras Theorem -

• Height = 15 m
• Hypotenuse = 113 m
• Base = ??

⇒ (Hypotenuse)² = (Base)² + (Height)²

⇒ (113)² = (x)² + (15)²

⇒ x² = 12769 - 225

⇒ x² = 12544

⇒ x = $\sf{\sqrt{12544}}$

⇒ x = 112 m

Radius of the circle = 112 m

$\rule{300}{1.5}$

★ Area under surveillance -

⇒ Area of circle = πr²

⇒ 22/7 × 112 × 112

⇒ 22/7 × 12554

⇒ 22 × 1792

⇒ 39424 m²

Area under surveillance = 39424 m²

Therefore, the CCTV covers 39242 m² of area.

Answer 2

$</p><p>\tt{\pink{\huge{Answer \: -15 \: m. }}}$

The Above Question is Incomplete.

$</p><p>\tt{\huge{\boxed{\boxed{\bullet{\green{Correct \: Question \: - }}}}}}$

For traffic control, a CCTV camera is fixed on a straight and vertical pole.

The camera can see 113m distance straight line from the top.

If the area visible by the camera around the pole is $39424 \: {m}^2$ , then find the height of the pole.

$</p><p>\tt{\orange{Step-By-Step-Explaination \: : }}$

$</p><p>\tt{\red{Area \: Surrounded \: = 39429 \: {cm}^2 }}$

$\tt{ \purple{ \therefore{\pi \: {r}^{2} = 39429 \: }}}$

$\tt{ \orange{ \implies{r \: = 112 \: cm. \: }}}$

Let The Height Of The Pole Be H m.

By Pythagoras Theorem, we can state that :

$\tt{ \blue{ \implies{ {r}^{2} + {h}^{2} = {113}^{2} }}}$

Solving we get H = 15 m.

Hence, the required height of the pole is 15 m.

$</p><p>\tt{\purple{------------- }}$