A smaller circle has radius of r units and a larger circle has a radius of s uni...

Questions

September 2022 1 6 Report

A smaller circle has radius of r units and a larger circle has a radius of s units. What is the factored form of the positive difference between their areas?

Answers & Comments

KuyaEngr

Verified answer

Area of Plane Figure and Factoring Polynomials

The given problem is an application of solving area of the plane figure in real life situation. You will apply your basic knowledge in mathematics and geometry especially in solving area of rectangle and how many items can be occupied in the space provided and identifying it's dimensions.

The given problem, "A smaller circle has radius of r units and a larger circle has a radius of s units. What is the factored form of the positive difference between their areas?"

Solution and Discussion

In mathematics, solving area of plane figure is commonly used in architectural and construction industry including floor covering, such as carpets and tiles. Calculation of dimensions and area measurements applied in wallpaper and paint. Solving area also applied in industry including machineries, clothing and other items that used length and width of the figure.

How to find the area of a circle? Area of a square is the space occupied by the shape express in square units. Finding area is the product of constant π and square of radius (A = πr²).

Step-by-step Solution

Step 1: Identify all the given in the problem

A smaller circle has radius of r units

A larger circle has a radius of s units

Step 2: Identify what is being ask

What is the factored form of the positive difference between their areas?

Step 3: Create mathematical equation using the formula.

A = πr², when r = r units → smaller

A = πs², when r = s units → larger circle

Difference of two area of circle

→ (πs²) - (πr²)

Step 4: Factoring the equation

What is Factoring

Factoring is the method on how to rewrite a polynomial into simpler factors, and by equating these factors to zero.

Read more about factoring here at brainly.ph/question/17564689

Now, factor out (πs²) - (πr²)

(πs²) - (πr²)

→ (π)(s² - r²), assume s is greater than r. As stated above, the larger circle is having a radius s units.

Thus, the factored form of the positive difference between their areas is (π)(s² - r²).

Tips in Solving Math problems

Apply your knowledge in previous topics.
Don't forget the units of the problem, convert the unit first if necessary before you jump in the solution.
Check the solution
Practice and practice solving word problems