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From a circular piece of carboard of radius \( 3 \mathrm{~cm} \) two sectors of \( 90^{\circ} \) have been cut off. Find the perimeter of the remaining portion nearest hundredth centimeters (Take \( \pi=22 / 7) \)
Given:
From a circular piece of carboard of radius \( 3 \mathrm{~cm} \) two sectors of \( 90^{\circ} \) have been cut off.
To do:
We have to find the perimeter of the remaining portion nearest the hundredth centimetres.
Solution:
Let $ABCD$ be the cardboard as shown in the figure.
Two sectors of \( 90^{\circ} \) have been cut off.
This implies,
We get a semicular cardboard piece.
Let $ABD$ be the remaining cardboard piece.
Therefore,
Perimeter of arc $ABD=\frac{1}{2}(2 \pi r)$
$=\pi (3)$
$=\frac{22}{7} \times 3$
$=\frac{66}{7}$
$=9.428 \mathrm{~cm}$
The perimeter of the remaining portion nearest hundredth centimeters is $9.428 \mathrm{~cm}$.