Question

A hemisphere-shpaped ole has a diameter of 5.7 millimeters and a surface area of about 51 square millimeters. The radius of the mole doubls. Estimate the new surface area of the mole.

Answer 1

Step 1: Calculate the diameter of mole

When radius gets doubled then diameter gets also doubled

So diameter of new mole

$$\begin{gathered} =5.7\times 2=11.4\mathrm{mm} \\ \frac{\mathrm{Surface}\mathrm{area}\mathrm{of}\mathrm{old}\mathrm{mole}}{\mathrm{Surface}\mathrm{Area}\mathrm{of}\mathrm{large}\mathrm{mole}}={\left(\frac{\mathrm{Diameter}\mathrm{of}\mathrm{mole}1}{\mathrm{Diameter}\mathrm{of}\mathrm{mole}2}\right)}^2 \end{gathered}$$

Step 2: Calculate the surface area of larger mole

$$\begin{gathered} \frac{51}{\mathrm{s}}={\left(\frac{5.7}{11.4}\right)}^2 \\ \frac{51}{\mathrm{s}}=\frac{1}{4} \\ \mathrm{S}\times 1=51\times 4 \\ \mathrm{S}=204 \end{gathered}$$

So, surface area of larger mole is $204{\mathrm{mm}}^2$
Hence, Surface area of large mole is $204{\mathrm{mm}}^2$