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Maths-

General

Easy

Question

The shaded portion in the given figure shows a circular path enclosed by the two concentric circles. If the inner circumference of the path is 176 m and the uniform width of the circular path is 3.5 m, find the area of the path

hint Hint:

Area of the path is the difference of the areas of two circles

The correct answer is: 346.5 m2

It is given that Inner circumference of the path= 176 m
$rightwards double arrow$ 2 $straight pi$ r = 172 r = 176
r = 14 m
Radius of outer circle = Radius of inner circle + Width of path
= (14 + 3.5 ) m
= 17.5 m
We know that Area of a circle = $straight pi$ r²
Area of the path = Area of outer circle – Area of inner circle
= $22 over 7$ × (17.5)² - $22 over 7$ × 14²
= $22 over 7$ ( 17.5 – 14)(17.5 + 14)
( $therefore$ a² – b²) = (a – b)(a + b)
= $22 over 7$ × 3.5 × 31.5
= 346.5 m²

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