Pac-Man in 2D

Geometry Level pending

A yellow character from a well-known video game franchise has a circular shape. By opening his mouth, he forms a circular sector with a radius of $x\text{ cm}$ .

If the arc corresponding to this sector also has a length of $x\text{ cm}$ , find the area of yellow region (the character's body).

Try solving Pac-Man in 3D !

This problem is original.

Image Credit: Prickätarpucken by Balthazar, Wikipedia .

{ { x }^{ 2 } }\left( \pi -\frac { \sqrt { 3 } }{ 2 } \right) \text{ cm }^{ 2 }

{ x }^{ 2 }\left( \pi -\frac { 1 }{ 2 } \right) \text{ cm }^{ 2 }

{ x }\left( x\pi -\frac { 1 }{ 2 } \right) \text{ cm }^{ 2 }

{ x }\left( 4x\pi -\frac { 1 }{ 4 } \right) \text{ cm }^{ 2 }

{ x }^{ 2 }\left( \pi -\frac { 1 }{ 4 } \right) \text{ cm }^{ 2 }

1 solution

Ahmad Saad
Jan 27, 2017

Pac-Man in 2D

Try solving Pac-Man in 3D !

This problem is original.

Image Credit: Prickätarpucken by Balthazar, Wikipedia .

1 solution

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