Question

The total surface area of solid hemisphere of diameter 2 cm is equal to
$
  {\text{A}}{\text{. }}12{\text{ c}}{{\text{m}}^2} \\
  {\text{B}}{\text{. }}12\pi {\text{ c}}{{\text{m}}^2} \\
  {\text{C}}{\text{. 4}}\pi {\text{ c}}{{\text{m}}^2} \\
  {\text{D}}{\text{. 3}}\pi {\text{ c}}{{\text{m}}^2} \\
$

Answer 1

Hint – Total surface area of the solid hemisphere is given as$3\pi {r^2}$, so use this formula to reach the answer, where symbols have their usual meaning.

It is given that the diameter of the hemisphere $ = 2{\text{ cm}}$
Therefore radius (r) of the hemisphere $ = \dfrac{{{\text{Diameter}}}}{2} = \dfrac{2}{2} = 1{\text{ cm}}$
Now as we know that the total surface area (S.A) of the solid hemisphere $ = 3\pi {r^2}$, where r is the radius of the hemisphere.
$ \Rightarrow S.A = 3\pi {r^2} = 3\pi {\left( 1 \right)^2} = 3\pi $.
Hence, option (d) is correct.

Note – whenever we face such types of problems the key concept we have to remember is that always recall the formula of surface area of solid hemisphere which is stated above, then in this formula put the value of radius as above, we will get the required answer.