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 1.8π m².\n(type an exact answer, using π as needed.)\nb. the estimated change in area is □% of the circles original area.\n(type an integer or a decimal. do not round.)
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=2\pi rdr). Here, (r = 10) (original radius) and (dr=0.09) (change in radius).
Step2: Calculate the original area
The original area (A_{0}=\pi r^{2}=\pi\times(10)^{2}=100\pi).
Step3: Calculate the percentage change
We know from part (a) that (dA = 1.8\pi). The percentage change is (\frac{dA}{A_{0}}\times100). Substitute (dA = 1.8\pi) and (A_{0}=100\pi) into the formula: (\frac{1.8\pi}{100\pi}\times 100).
Answer:
(1.8)