The four equal circles of radius 4 cm drawn on the four

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The four equal circles of radius 4 cm drawn on the four corners of a square touch each other externally. Then the area of the portion between the square and the four sectors is

1. 9 (π – 4) sq. cm.
2. 16 (π – 4) sq. cm.
3. 9 (4 – π) sq. cm.
4. 16 (4 – π) sq.cm.

Correct Option: D

Using Rule 10 and 14,

Side of the square = 8 cm
∴ Area of the square = 8 × 8 = 64 sq.cm.
Area of the four sectors = π × 4² = 16π sq.cm.
∴ Required area = 64 – 16π
= 16 (4 – π) sq.cm.