Question

A CCTV camera has installed on the top of a straight pole of 8m height such that forward traffic can be seen from the line of sight 10m . Find the area of circular path formed by Shadow around the pole.(π =3.14 )
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Answer 1

Given:

The height of the straight pole = 8 m

The distance from which the forward traffic can be seen from the line of sight = 10 m

To find:

The area of the circular path formed by shadow around the pole

Solution:

Referring to the figure attached below, let's assume,

OB = radius of the circular path formed by the shadow around the pole

AO = height of the pole = 8 m

AB =  distance from which the forward traffic can be seen from the line of sight = 10 m

In ΔAOB, using the Pythagoras Theorem, we get

$AO^2 + OB^2 = AB^2$

substituting AO = 8 m & AB = 10 m

$\implies 8^2 + OB^2 = 10^2$

$\implies OB^2 = 10^2 - 8^2$

$\implies OB= \sqrt{100 - 64}$

$\implies OB= \sqrt{36}$

$\implies \bold{OB= 6 \:m}$

We know the formula of the area of a circle is given as:

$\boxed{\bold{Area = \pi r^2}}$

Here

$\pi$ = 3.14

r = OB = 6 m

Now, using the formula above we get,

The area of the circular path formed by the shadow around the pole is,

= $3.14 \times 6^2$

= $3.14 \times 36$

= $\bold{113.04\:m^2}$

Thus, the area of the circular path formed by Shadow around the pole is 113.04 m².

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Also View:

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at a certain time a tree 6m High casts a shadow of length 8 metres at the same time a pole casts a shadow of length 20 m find the height of the pole

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Answer 2

Required Solution:-

[See the Diagram attached above ! ]

• Height of Straight Pole, OY = 8 m
• Distance from which forward traffic can be seen from the line of sight, XY = 10m

To Find:-

• 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

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