Chapter 4 - Differentiation - 4.1 Linear Approximation and Applications - Exercises - Page 173: 41

Volume = $3927$ $cm^{3}$ Surface = $314.2$ $cm^{2}$

Volume $V(r)$ = $\frac{4}{3}\pi{r^{3}}$ $V'(r)$ = $4\pi{r^{2}}$ $V'(r)$ = $\frac{ΔV}{Δr}$ $ΔV$ = $V'(r)Δr$ $ΔV$ = $4\pi{(25)^{2}}(0.5)$ = $3927$ $cm^{3}$ Surface $V(r)$ = $4\pi{r^{2}}$ $V'(r)$ = $8\pi{r}$ $V'(r)$ = $\frac{ΔV}{Δr}$ $ΔV$ = $V'(r)Δr$ $ΔV$ = $8\pi{(25)}(0.5)$ = $314.2$ $cm^{2}$