Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Wire of Length x

A wire of length x is bent into the shape of a circle.

A. Express the circumference C of the circle as a function of x.

B. Express the area A of the circle as a function of x.

Let me see.

Part A

Circumference of circle = pi•d, where d is diameter, which can also be expressed as 2r•pi, where r = radius of circle. We want C(x).

Let C = length x

x = 2r•pi

Solve for r.

x/2•pi = r....plug into circumference of circle formula.

C = 2r•pi

We want C(x).

C(x) = 2(x/2•pi)(pi)

C(x) = x

You say?

Part B

From part A, I know that r = x/2•pi.

We want A(x).

Area of circle = pi•r^2.

A(x) = pi(x/2•pi)^2

A(x) = pi(x^2/4•pi^2)

A(x) = x^2/(4•pi)

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Wire of Length x

Both parts good.

Bob

---

Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Wire of Length x

Both parts good.

Bob

I don't know how I got this right. I greatly struggle with forming mathematical models.