Question

Find the total surface area of a hollow hemisphere whose outer and inner radii are 4.2cm and 2.1cm respectively.

Answer 1

Hint: It is just a formula application. Remember the formula for Total Surface area of Hollow Hemisphere & you’ll get the answer.

Complete step by step answer:

Total Surface area of Hollow Hemisphere is, $2\pi \left( {{r_1}^2 + {r_2}^2} \right)+ \pi \left( {{r_1}^2 - {r_2}^2} \right)$

$=3\pi \left( {{r_1}^2} \right)+ \pi \left( {{r_2}^2} \right)$

Where ${r_1}$ is outer radii and ${r_2}$ is inner radii.

So, according to question

${r_1}$ = 4.2cm

${r_2}$ = 2.1cm 

$\Rightarrow {\text{Area }}\left( {\text{A}} \right) =3\pi \left( {{4.2}^2} \right)+ \pi \left( {{2.1}^2} \right) $

$\Rightarrow {\text{A = }}\pi \left( {52.92} \right)+ \pi \left( {4.41} \right)$

$\Rightarrow {\text{A = }} \dfrac{{22}}{7} \times 57.33$

$\Rightarrow {\text{A = 180}}{\text{.18}}\;{\text{sq}}{\text{.cm}}$

So, this is your answer.

Note: Remember the formula of surface area and then calculate using the formula, you will get your answer. Don’t get confused between two formulas.