How JustAnswer Works:

  • Ask an Expert
    Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.
  • Get a Professional Answer
    Via email, text message, or notification as you wait on our site.
    Ask follow up questions if you need to.
  • 100% Satisfaction Guarantee
    Rate the answer you receive.

Ask namstech Your Own Question

namstech
namstech, Electrical Engineer
Category: Math Homework
Satisfied Customers: 2124
Experience:  M.S. Signals and Information Processing
Type Your Math Homework Question Here...
namstech is online now
A new question is answered every 9 seconds

Choose one of the following scenarios, explain your reasoning

Customer Question

Choose one of the following scenarios, explain your reasoning and provide an example that demonstrates your logic.
Ø What happens to the circumference of a circle if you double the radius? What happens if you double the diameter? What happens if you triple the radius?
Ø What happens to the area of a circle if you double the radius? What happens if you double the diameter? What happens if you triple the radius?
Ø What is the effect on the area of a triangle if the base is doubled and the height is cut in half? What happens to the area, if the base is doubled and the height remains the same?
Submitted: 1 year ago.
Category: Math Homework
Expert:  namstech replied 1 year ago.

Hello and welcome to JustAnswer!

Q) What happens to the circumference of a circle if you double the radius? What happens if you double the diameter? What happens if you triple the radius?

SOLUTION:

Circumference = 2πr

- Let r1 be a radius, then circumference c1 is given as

c1 = 2πr1

If r2 = 2r1 (radius doubled), then

c2 = 2πr2 = 2π(2r1) = 2(2πr1) = 2c1

Hence when radius is doubled, circumference is doubled.

- In terms of diameter d, circumference is given as:

circumference = πd

For diameter d1, circumference c1 is given as

c1 = πd1

If d2 = 2d1, then

c2 = πd2 = π(2d1) = 2πd1 = 2c1

Hence when the diameter is doubled, circumference doubles.

If r3 = 3r1, then

c3 = 2πr3 = 2π(3r1) = 3 (2πr1) = 3c1

Hence, when radius is tripled, circumference triples.

Q) What happens to the area of a circle if you double the radius? What happens if you double the diameter? What happens if you triple the radius?

SOLUTION:

Area = π (radius)^2

If r1 is radius, then

A1 = π (r1)^2

If r2 = 2r1, then

A2 = π (r2)^2 = π (2r1)^2 = 4 π (r1)^2 = 4 A1

If radius is doubled, then area is quadrupled.

In terms of diameter, area of circle is given as

Area = π (d/2)^2 = (π/4) d^2

Let d1 be a diameter, then

A1 = (π/4) (d1)^2

Let d2 = 2d1, then

A2 = (π/4)(d2)^2 = (π/4)(2d1)^2 = 4(π/4)(d1)^2 = 4A1

Hence, when the diameter is doubled, area is quadrupled.

Now, if r3 = 3r1, then

A3 = π(r3)^2 = π(3r1)^2 = 9 π(r1)^2 = 9A1

Hence, when the radius is tripled, area increases 9 times.


Q) What is the effect on the area of a triangle if the base is doubled and the height is cut in half? What happens to the area, if the base is doubled and the height remains the same?

SOLUTION:

Area of triangle = (1/2)(base)(height)

Let b1 and h1 be heights, then

A1 = (1/2)(b1)(h1)

Now if b2 = 2b1 and h2 = (h1/2)

Then

A2 = (1/2)(b2)(h2) = (1/2)(2b1)(h1/2) = (1/2)(b1)(h1) = A1

Hence when the base is doubled and height is halved, area of the triangle remains the same.

Now if b3 = 2b1 and h3 = h1, then

A3 = (1/2)(b3)(h3) = (1/2)(2b1)(h1) = 2 (1/2)(b1)(h1) = 2A1

That shows that when base is doubled but the height remains the same, area of the triangle is doubled.

namstech, Electrical Engineer
Category: Math Homework
Satisfied Customers: 2124
Experience: M.S. Signals and Information Processing
namstech and 2 other Math Homework Specialists are ready to help you
Customer: replied 1 year ago.
where do the "4" and "9" come from in your area formulas?
Expert:  namstech replied 1 year ago.
You are probably referring to the following part:

If r2 = 2r1, then
A2 = π (r2)^2 = π (2r1)^2 = 4 π (r1)^2 = 4 A1

Here, new radius r2 is double than that of radius r1. Now when you put that value in the formula, we get square of the value 2r1, whose square is 4r1^2 (i.e. square of 2 and square of r1^2). That is how we get 4 in the formula. Same argument goes for the radius r3 that is 3 times r1 i.e. 3r1^2. Squaring it in the formula yields the value 9r1^2 and hence we have 9 in the area.

I hope this helps. If there is still some confusion, please don't hesitate to ask.

Regards

JustAnswer in the News:

 
 
 
Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.
JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.
Web sites like justanswer.com/legal
...leave nothing to chance.
Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.
Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.
I will tell you that...the things you have to go through to be an Expert are quite rigorous.
 
 
 

What Customers are Saying:

 
 
 
  • Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C. Freshfield, Liverpool, UK
< Last | Next >
  • Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C. Freshfield, Liverpool, UK
  • This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!! Alex Los Angeles, CA
  • Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult. GP Hesperia, CA
  • I couldn't be more satisfied! This is the site I will always come to when I need a second opinion. Justin Kernersville, NC
  • Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around. Esther Woodstock, NY
  • Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know. Robin Elkton, Maryland
  • He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here. Diane Dallas, TX
 
 
 

Meet The Experts:

 
 
 
  • Mr. Gregory White's Avatar

    Mr. Gregory White

    Master's Degree

    Satisfied Customers:

    84
    M.A., M.S. Education / Educational Administration
< Last | Next >
  • http://ww2.justanswer.com/uploads/ED/educatortech/2012-6-7_1256_williams4.64x64.jpg Mr. Gregory White's Avatar

    Mr. Gregory White

    Master's Degree

    Satisfied Customers:

    84
    M.A., M.S. Education / Educational Administration
  • http://ww2.justanswer.com/uploads/SO/sonofGauss/2012-6-6_20151_PortraitLHW.64x64.jpg JACUSTOMER-yrynbdjl-'s Avatar

    JACUSTOMER-yrynbdjl-

    Master's Degree

    Satisfied Customers:

    49
    I have taught college Mathematics for the past 10 years.
  • http://ww2.justanswer.com/uploads/CO/CosumelEyes/2012-5-4_4923_Profile.64x64.jpg Ray Atkinson's Avatar

    Ray Atkinson

    Bachelor's Degree

    Satisfied Customers:

    43
    Grad student. Years and years of tutoring. Education, accounting, and math degrees.
  • http://ww2.justanswer.com/uploads/homeworklady/2008-11-24_125231_susannewavatar.jpg SusanAthena's Avatar

    SusanAthena

    Master's Degree

    Satisfied Customers:

    29
    Tutor for Algebra, Geometry, Statistics. Explaining math in plain English.
  • http://ww2.justanswer.com/uploads/mhasan420/2010-1-23_19189_topi.jpg mhasan420's Avatar

    mhasan420

    Master's Degree

    Satisfied Customers:

    29
    BA Maths, Oxford
  • http://ww2.justanswer.com/uploads/AR/arubin9/2012-2-4_42617_ArthurRubinedit.64x64.jpg Dr Arthur Rubin's Avatar

    Dr Arthur Rubin

    Doctoral Degree

    Satisfied Customers:

    26
    Ph.D. in Mathematics, California Institute of Technology
  • http://ww2.justanswer.com/uploads/DO/Donbacongamer/2012-3-6_2337_mathmaster.64x64.jpg Don's Avatar

    Don

    Master's Degree

    Satisfied Customers:

    17
    M.S. Astronautical Engineering. Math/Science/Comp Tutor