the radius of a circle is increased from 10.00 to 10.09 m.\na. estimate the resulting change in area.\nb…

the radius of a circle is increased from 10.00 to 10.09 m.\na. estimate the resulting change in area.\nb. express the estimate as a percentage of the circles original area.\na. the estimated change in area is \n(type an exact answer, using π as needed.)

the radius of a circle is increased from 10.00 to 10.09 m.\na. estimate the resulting change in area.\nb. express the estimate as a percentage of the circles original area.\na. the estimated change in area is \n(type an exact answer, using π as needed.)

Answer

Explanation:

Step1: Recall the formula for the area of a circle

The area of a circle is (A = \pi r^{2}). The differential (dA) is given by (dA=A^{\prime}(r)dr). Differentiating (A(r)=\pi r^{2}) with respect to (r), we get (A^{\prime}(r) = 2\pi r).

Step2: Identify the values of (r) and (dr)

We are given that (r = 10.00) m and (dr=\Delta r=10.09 - 10.00=0.09) m.

Step3: Calculate the differential (dA)

Substitute (r = 10) and (dr = 0.09) into the formula (dA=2\pi rdr). [ \begin{align*} dA&=2\pi\times10\times0.09\ &=1.8\pi \end{align*} ]

Answer:

(1.8\pi)