1. ## Worded max/min problem

A piece of wire 20cm long is cut into two pieces. One piece is used for a square shape and the other a circle shape with radius r cm.

i) write down the area and the perimeter of the circle in terms of r.
I would go
A = ∏r^2
A/r^2 =
r^2 = A/
r = sqrt(A/∏)

P = 2∏r
r = P/2
But not sure if this is right

ii) find the perimeter of the square in terms of r
iii) using your answer in part ii) state the length of one side of the square in terms of r.
iv) find the area of the square in terms of r
v) find the total area A cm^2 of the circle and the square in terms of r
i'm unsure how to do these one any help would be greatly appreciated!!

2. ## Word problem

Hello scubasteve94
Originally Posted by scubasteve94
A piece of wire 20cm long is cut into two pieces. One piece is used for a square shape and the other a circle shape with radius r cm.

i) write down the area and the perimeter of the circle in terms of r.
I would go
A = ∏r^2
A/r^2 =
r^2 = A/
r = sqrt(A/∏)

P = 2∏r
r = P/2
But not sure if this is right

ii) find the perimeter of the square in terms of r
iii) using your answer in part ii) state the length of one side of the square in terms of r.
iv) find the area of the square in terms of r
v) find the total area A cm^2 of the circle and the square in terms of r
i'm unsure how to do these one any help would be greatly appreciated!!
In part (i), you have the right formulae for $A$ and $P$, but you don't need to change them around to make $r$ the subject. Just leave them as:

$A = \pi r^2$ and $P = 2\pi r$

(ii) The key fact you have to use for the next bit is that if you have used $P$ cm to make the circle ( $= 2\pi r$) then you'll have $(20-P)$ cm of wire left to make the square. So that's the perimeter of the square. But we want it in terms of $r$, so we simply say: the perimeter of the square is $(20 - 2\pi r)$ cm.

(iii) How do you find the length of one side of a square if you know its perimeter? Well just do that to $(20 - 2\pi r)$ and there's the answer. (Note: in algebra, when you're dividing by something, it's often easiest to write the result as a fraction. So $a \div b$, for instance, is usually written $\frac{a}{b}$.}

Can you complete it now?

3. Originally Posted by scubasteve94
A piece of wire 20cm long is cut into two pieces. One piece is used for a square shape and the other a circle shape with radius r cm.

i) write down the area and the perimeter of the circle in terms of r.
I would go
A = ∏r^2
A/r^2 =
r^2 = A/
r = sqrt(A/∏)

P = 2∏r
r = P/2
But not sure if this is right

ii) find the perimeter of the square in terms of r
iii) using your answer in part ii) state the length of one side of the square in terms of r.
iv) find the area of the square in terms of r
v) find the total area A cm^2 of the circle and the square in terms of r
i'm unsure how to do these one any help would be greatly appreciated!!