Very Interesting....Did You Know?

[~Sassy~]

A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r? (p=> Pi)

A. pr2
B. pr2 + 10
C. pr2 + ¼ p2r2
D. pr2 + (40-2pr)2
E. pr2 + (10- ½ pr)2

Area of the circle = pi * r^2
Length of left-out wire = 40 - 2*pi*r (The reason behind this is that the circumference will give you the left-out length of the wire.)

If length of the square = a
4a = 40 - 2*pi*r
a = 10 - 1/2*pi*r
So area of the square = a^2 = (10 - 1/2*pi*r) ^ 2
So sum-up = pi * r^2 + (10 - 1/2*pi*r) ^ 2.

The answer is D.
The main reason here is the length of the wire should be equal to the circumference of the objects produced.

It is amazing what you can find on Google. 

[Stinkerbell]

Area of the circle = pi * r^2
Length of left-out wire = 40 - 2*pi*r (The reason behind this is that the circumference will give you the left-out length of the wire.)

If length of the square = a
4a = 40 - 2*pi*r
a = 10 - 1/2*pi*r
So area of the square = a^2 = (10 - 1/2*pi*r) ^ 2
So sum-up = pi * r^2 + (10 - 1/2*pi*r) ^ 2.

The answer is D.
The main reason here is the length of the wire should be equal to the circumference of the objects produced.

It is amazing what you can find on Google. 

Smart a$$    Why not just be a suck up like me?

[jarjar]

Smart a$$    Why not just be a suck up like me?

[Squid]

 

[~Sassy~]

Smart a$$    Why not just be a suck up like me?

One of you ... and one of me is enough. 

[Squid]

 

[Stinkerbell]

One of you ... and one of me is enough. 

[Hocky]

What if there was a smart a$$ suck up?  Who would that be? 

[Stinkerbell]

What if there was a smart a$$ suck up?  Who would that be? 

You just volunteered for the job! Welcome to the club! 

[Hocky]

You just volunteered for the job! Welcome to the club! 

Who lil 'ol me? 

Thank you........I think......

[disneyland lady]

Thankfully Sassy has our back when it comes to math. My excuse is that it is Spring Break (somewhere) and I am sure I would get this problem as soon as I go back to/or get some class.

[Stinkerbell]

A thin piece of wire 40 meters long is cut into two pieces. One piece is used to form a circle with radius r, and the other is used to form a square. No wire is left over. Which of the following represents the total area, in square meters, of the circular and the square regions in terms of r? (p=> Pi)

A. pr2
B. pr2 + 10
C. pr2 + ¼ p2r2
D. pr2 + (40-2pr)2
E. pr2 + (10- ½ pr)2
F. One of the above!

F. One of the above!

I KNOW that's the right answer!