SOLUTION: I tried to answer this question and the correct answer according to the answer book was: 8 times r^2 times pi meters squared. Here's the problem: "In the figure shown, if the small

Question 1083421: I tried to answer this question and the correct answer according to the answer book was: 8 times r^2 times pi meters squared. Here's the problem: "In the figure shown, if the small circle inside the larger one has a radius of "r" meters and the larger circle has a diameter of "6r" meters, what is the area of the region inside the large circle and outside the small circle?" My process and answer: The area of the small circle is r^2 times pi meters squared. The area of the large circle is 3r^2 times pi meters squared. Subtract the small circle from the large circle to get 2r^2 times pi meters squared. Where did I go wrong?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let's refer to the two areas as A1 and A2, where
A1 = area of small circle
A2 = area of large circle

area of small circle:
A1 = pi*(small circle radius)^2
A1 = pi*(r)^2
A1 = pi*r^2

Area of large circle
A2 = pi*(large circle radius)^2
A2 = pi*(3r)^2 ... ** see note below **
A2 = pi*(3r)*(3r)
A2 = pi*(9r^2)
A2 = 9pi*r^2

note: radius = diameter/2 = 6r/2 = 3r

Subtract the areas to get the difference D
D = A2 - A1
D = 9pi*r^2 - pi*r^2
D = (9pi - pi)*r^2
D = 8pi*r^2
which is the area of the region outside of the small circle but inside the larger circle.

8*pi*r^2 is the same as 8*r^2*pi. The order of which you multiply the terms doesn't matter.

RELATED QUESTIONS
Hello again friends. I have a Calculus question. I would really appreciate the help. I... (answered by Fombitz)

I have a math problem where pi=22/7 and i have to find the area of a circle using pi with (answered by Fombitz,nerdybill)

this question is about order of operations. i have a book called Painless Algerbra, and... (answered by queenofit)

6x^2 - 28x + 16 x^4 + 2x^3 - 3x - 6 x^8 - 1 If I am doing it correctly and... (answered by jim_thompson5910,solver91311,stanbon)

linda reads 1/5 of a book on friday and 2/7 of the book on saturday. On sunday she read... (answered by rfer)

I was giving an interview test earlier today. The job doesn't require a high level of... (answered by ankor@dixie-net.com,scott8148)

This is my last question that I need an answer for. I tried many times but the answer was (answered by josmiceli)

I have tried to simplify this problem 4 different ways but cannot match the answer in the (answered by Alan3354)

Write the following expression without using the factorial symbol. nC3 + nC2 + nC1... (answered by Boreal)