Question

Find the total surface area of a hemisphere of radius 10 cm. \[\left( \text{Use }\pi =3.14 \right)\]

Answer 1

Hint: Apply the formula for total surface area of the hemisphere. Total surface area of the hemisphere is equal to the sum of lateral surface area of the hemisphere and the area of the circular base of the hemisphere.

Complete step-by-step answer:
A solid hemisphere is obtained when we cut a solid sphere into two equal halves. The volume of the hemisphere is half that of the volume of the sphere. The prefix ‘hemi’ means half. So, a hemisphere is a three-dimensional shape that is half of a sphere with one flat circular side which is also known as the face of the hemisphere. In the real world, we will find hemispheres all around us. There are three types of hemisphere. First one is a hollow hemisphere which has only a lateral surface. Second one is a solid hemisphere that has a circular base in addition to the lateral surface. Last but not the least, the third one is a hemispherical shell defined as the solid enclosed between two concentric hemispheres. In the above question we have to find the total surface area of the hemisphere, so we will consider it as a solid hemisphere.
We know that the lateral surface area of the hemisphere is $2\pi {{r}^{2}}$. In the solid hemisphere its circular base is present whose area is $\pi {{r}^{2}}$. Hence, the total surface area of solid hemisphere is, $2\pi {{r}^{2}}+\pi {{r}^{2}}=3\pi {{r}^{2}}$.
Therefore, total surface area of the given hemisphere
$\begin{align}
  & =3\times 3.14\times {{10}^{2}} \\
 & =942\text{ c}{{\text{m}}^{2}} \\
\end{align}$
Hence, the total surface area of the given hemisphere is $942\text{ c}{{\text{m}}^{2}}$.

Note: We have used the value of $\pi $ equal to 3.14 because it is provided in the question. Also, we have assumed the hemisphere as a solid one because in the question the total surface area is asked and the hollow hemisphere has only lateral surface.