Mathematics - Application of Derivative Question with Solution | TestHub

Volume of sphere $\mathrm{V}=\frac{4}{3}\pi r^3$ $\frac{d\mathrm{V}}{dt}=\frac{4}{3}\cdot \pi \cdot 3r^2\cdot \frac{dr}{dt}$ $35=4\pi r^2\cdot \frac{dr}{dt}$ or $\frac{dr}{dt}=\frac{35}{4\pi r^2}$ Surface area of sphere $=\mathrm{S}=4\pi r^2$ $\frac{d\mathrm{S}}{dt}=4\pi \times 2r\times \frac{dr}{dt}=8\pi r\cdot \frac{dr}{dt}$ $\frac{d\mathrm{S}}{dt}=\frac{70}{r}$ Now, diameter $=14\mathrm{cm},r=7$ $\therefore \frac{d\mathrm{S}}{dt}=10$