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Volume and surface area of a tumor The diameter of a tumor was measured to be 19 $\mathrm{mm}$ . If the diameter increases by 1 $\mathrm{mm}$ , use linear approximations to estimate the relative changes in the volume $\left(V=\frac{4}{3} \pi r^{3}\right)$ and surface area $\left(S=4 \pi r^{2}\right) .$

Relative Change in Volume: 16$\%$Relative Change in Area: 11$\%$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Missouri State University

Oregon State University

Baylor University

Lectures

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The volume of a sphere is …

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$V=\frac{4}{3} \pi r^{3} ;…

Surface Area The change in…

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