Question

a wire of length 3x is bent into the shape of a circle. A. Express the circumference of the circle as a function of x. B. Express the area of the circle as a function of x.

Answer 1

Answer:

A.

B.   

Explanation:

(A) Since, the wire of length 3x is bent into the shape of a circle. So, the circumference of the circle made by the wire will be the total length of the wire, i.e. 3x.

So, let S denote the circumference of the circle. So,

------------------------------------------- (1)

This is the expression of circumference of the circle as a function of x

(B) let the radius of the circle be r. So, circumference (S) will be given by the following expression.

Using eqn 1

Now, the area, A, of the circle is given by the expression.

Substituting the value of r

This is the expression of area of the circle as a function of x