Urgent 2

Question

you have been asked to draw the largest circle possible on a square piece of paper that have a length of 4x unit. Draw a diagram of this. And show how to use a rational expression to compare the area of the circle to the area of square piece of paper. Simplify Rational Expression. What is the percent of the square piece of paper is cover by a circle.

 

Answer 1

Side of square the piece of paper = 4x

The largest circle possible on a square piece which will touches all sides of the square as shown in figure.

So Diameter of the circle equals to Side of the square piece of paper.

Diameter of the largest circle d = 4x

Radius of the largest circle r = d/2 = 4x/2 = 2x

Area of the largest circle A_circle = πr²

A_circle = π(2x)² = π(4x²) = 4πx²

Area of the square piece A_square = (4x)(4x) = 16x²

 

The percent of the square piece of paper is cover by a circle = (Area of the largest circle)/( Area of the square piece)

= (A_circle) / (A_square)

= (4πx²) / (16x²)

= π / 4

= 0.7854 = 78.54 %

78.54 Percent of the square piece of paper is cover by a circle.