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Maths-

General

Easy

Question

The diameter of the three circles in this figure are 21 cm, 14 cm and 7 cm. What is the area of the shaded region?

hint Hint:

To find the area of shaded region subtract the area of circles inside from the outer circle.

The correct answer is: 154 cm2

The diameters of three circle in the figure is given.
Diameter of outer circle = 21 cm
$rightwards double arrow$ Radius = $fraction numerator text diameter end text over denominator 2 end fraction$
= $21 over 2$ cm
Area of the outer circle = $straight pi$ r²
= $22 over 7$ × ( $21 over 2$ )²
= 346.5 cm²
Diameter of the larger circle inside = 14 cm
$rightwards double arrow$ Radius = $fraction numerator text diameter end text over denominator 2 end fraction$
= $14 over 2$ = 7 cm
Area of the larger circle inside = $straight pi$ r²
= $22 over 7$ × 7²
= 154 cm²
Diameter of the smaller circle inside = 7 cm
$rightwards double arrow$ Radius = $fraction numerator text diameter end text over denominator 2 end fraction$
= $7 over 2$ cm
Area of the smaller circle inside = $straight pi$ r²
$equals 22 over 7$ × ( $7 over 2$ )²
= 38.5 cm²
Area of the shaded region = Area of the outer circle - Area of the larger circle inside - Area of the smaller circle
= 346.5 cm² - 154 cm² - 38.5 cm²
= 154 cm²

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