Mensuration
- If the four equal circles of radius 3 cm touch each other externally, then the area of the region bounded by the four circles is
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Using Rule 10 and 17,
Area of the shaded region = Area of square of side
6cm – 4 × a right angled sector= 36 - 4 × π × 3² 4
= 36 - 9π = 9(4 - π)sq. cm.Correct Option: B
Using Rule 10 and 17,
Area of the shaded region = Area of square of side
6cm – 4 × a right angled sector= 36 - 4 × π × 3² 4
= 36 - 9π = 9(4 - π)sq. cm.
- The area of a circle is increased by 22 cm² when its radius is increased by 1 cm. The original radius of the circle is
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Using Rule 14,
π(r + 1)² – πr² = 22
⇒ π(r² + 2r + l - r²) = 22
⇒ 2πr + π = 22⇒ 22 (2r + 1) = 22 7
⇒ 2r + 1 = 7
⇒ 2r = 6
⇒ r = 3 cm.Correct Option: A
Using Rule 14,
π(r + 1)² – πr² = 22
⇒ π(r² + 2r + l - r²) = 22
⇒ 2πr + π = 22⇒ 22 (2r + 1) = 22 7
⇒ 2r + 1 = 7
⇒ 2r = 6
⇒ r = 3 cm.
