Question

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Answer 1

Question 7 :

Solution : It is given that the circumference of the outer circle is 132 cm and the circumference of the inner circle is 88 cm.


Now, subtracting the circumference of inner circle from the circumference of the other circle.

= > Circumference of outer circle - circumference of inner circle = 132 cm - 88 cm


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From the properties of circle,
Circumference of circle = 2πr, where r is the radius of the circle.
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= > 2πR - 2πr = 132 cm - 88 cm

= > 2π( R - r ) = 44 cm

$= > 2 \times \dfrac{22}{7} \times ( R - r) = 44 \: cm \\ \\ \\ = > ( R - r) =44 \times \frac{7}{22} \times \dfrac{1}{2} \: cm \\ \\ \\ = > ( R - r) = 1\times 7 \: cm \\ \\ = > ( R - r) = 7\: cm$


Therefore the numeric value of R - r is 7 cm.




Question : 8

Solution : It is given that a piece of wire is in the form of rectangle of 8.9 cm length and 54 mm broad. And being bent in the form of a circle.

Although the shape of wire is being changed, its length will be same.


Therefore,
Perimeter of rectangle = Circumference of the circle

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Perimeter of rectangle = 2( length + breadth )
Circumference of circle = 2πr [ π = 22 / 7 ]
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= > 2( 8.9 cm + 54 mm ) = 2 π r


Cancel 2 from both sides and convert 8.9 cm into mm.


= > ( 8.9 x 10 ) mm + 54 mm = π r

= > 89 mm + 54 mm = πr

= > 143 = ( 22 / 7 ) r

= > 143 x 7 / 22 = r

= > 45.5 mm = r


Therefore the radius of the circle is 45.5 mm.
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