33.}ddPV} 5 }ddV} 1}Vn2RnTb} 2 }aVn22}252}ddV}(an2V22)5}(0V22nnRbT)2}12an2V23}(Vn2RTnb)2}1}2Van32}34.}ddst} 5 }ddt}(4.9t2)59.8t}dd2t2s} 5 }ddt}(9.8t)59.835.}ddMR} 5 }ddM}3M21}C2}2 }M3}245 }ddM}1}C2}M22 }13}M325CM2M236.If the radius of a circle is changed by a very small amountDr, the change in the area can be thought of as a very thinstrip with length given by the circumference, 2pr, andwidth Dr. Therefore, the change in the area can be thoughtof as (2pr)(Dr), which means that the change in the areadivided by the change in the radius is just 2pr.37.If the radius of a sphere is changed by a very small amountDr, the change in the volume can be thought of as a verythin layer with an area given by the surface area, 4pr2, anda thickness given by Dr. Therefore, the change in thevolume can be thought of as (4pr2)(Dr), which means thatthe change in the volume divided by the change in theradius is just 4pr2.
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