Answer:
a ) 2 r, b ) A c : A sq = π : 4, c ) The table: Area of the circle: 4 π , 9 π, 16 π, 4 r² π // Length of 1 side of the square: 4, 6, 8, 4 r // Area of the square: 16, 36, 64, 16 r² // Ratio: π/4, π/4, π/4, π/4.
Step-by-step explanation:
a ) The side of the square is twice the radius of the circle.
Therefore 2 r .
b ) A circle : A square = r² π : 4 r² = π : 4 = π / 4 ( or 3.14 : 4 )
c ) The area of the circle: A ( 2 ) = 2² π = 4 π
A ( 3 ) = 3² π = 9 π
A ( 4 ) = 4² π = 16 π
A ( 2 r ) = ( 2 r )² π = 4 r² π
The length of 1 side of the square:
L ( 2 ) = 2 · 2 = 4
L ( 3 ) = 2 · 3 = 6
L ( 4 ) = 2 · 4 = 8
L ( 2 r ) = 2 · 2 r = 4 r
Area of the square: A ( 4 ) = 4² = 16, A ( 6 ) = 6² = 36, A ( 8 ) = 8² = 64, A ( 4 r ) = ( 4 r ) ² = 16 r²
Ratio: 4π : 16 = π/4
9 π : 36 = π/4
16 π : 64 = π/4
4 r² π / 16 r² = π/4
