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Q.

Find the area of a ring whose outer and inner radii are 19 cm and 16 cm respectively.

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a

330 cm2

b

310 cm2

c

320 cm2

d

350 cm2

answer is A.

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Detailed Solution

Let's say that the radius of the outer circle is r1=19 cm and the radius of the inner circle is r2=16cm .
The area of the ring will be given by:
Area of the ring = Area of the outer circle - Area of the inner circle.
Using the formula for the area of a circle, we get:
= πr12−πr22
Taking out π as the common factor:
= π(r12−r22)

= \frac{22}{7} (19^{2} - 16^{2})

Using the identity a2−b2=(a+b)(a−b) , we get:

= \frac{22}{7} (19 + 16) (19 - 16)

= \frac{22}{7} \times 35 \times 3

= 22 \times 5 \times 3

= 330 c m^{2}

Therefore, the correct answer option 1 is 330 cm2 .

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