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The length of a side of an equilateral triangle is 8 cm. The area of the region lying between the circumference and the incircle of the triangle is (Use π = 22/7)
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50 1 cm² 7 -
50 2 cm² 7 -
75 1 cm² 7 -
75 2 cm² 7
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Correct Option: B
Let AD ⊥ BC
∴ BD = 4 cm and
AB = 8 cm
∴ AD = √AB² - BD² = √8² - 4²
= √64 - 16 = √48
= 4√3cm
∴ OD = radius of the in circle
| = | × 4√3 cm = | ||
| 3 | √3 |
∴ Area of the in circle
| = π |  |  | ² | cm² = | π cm² | ||
| √3 | 3 |
AO = radius of circum-circle
| = | × 4√3 = | ||
| 3 | √3 |
∴ Area of the cirum-circle
| = π | | | ² | = | π cm² | ||
| √3 | 3 |
∴ Area of the required region
| = | | π - | π | | cm² | ||
| 3 | 3 |
| = | = 16π cm² | |
| 3 |
| = | = | = 50 | cm² | |||
| 7 | 7 | 7 |
