Question

33. Persevere with Problems The figure at the right is composed of a circle

and a square. The circle touches the square at the midpoints of the
four sides
cm
a. What is the length of one side of the square?
b. The formula A = r is used to find the area of a circle. The formula
A = 4 can be used to find the area of the square. Write the ratio of
the area of the circle to the area of the square in simplest form.
cComplete the table
៨
-៩)
2
3
Area of Grde (units)
122 ore
Length of 1 Side of
the Square
Area of Square
42 616
(Area of circle
Ratio
of square)
d. What can you conclude about the relationship between the areas of the
circle and the square?
2
Lesson 3 Multiply and Divide Monomials

Answer 1

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.

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