Question

Find the total surface area of a hemisphere of the radius $10cm$.

Answer 1

Hint: We are given the radius of the hemisphere in the question, so we can use the formula for total surface area of hemisphere = curved surface area + base area $=2\pi {{r}^{2}}+\pi {{r}^{2}}$.

Complete Step-by-step answer:
Before proceeding with the question, we must know what is meant by hemisphere. A hemisphere is defined as a set of points in three-dimension and all points lying on the surface are equidistant from the centre. When a plane cuts across the sphere at the centre or equal parts, it forms a hemisphere. We can say that a hemisphere is exactly half of a sphere. We must know that the total surface area of a hemisphere = curved surface area + base area, where the base of the hemisphere is circular.
Here we have to find out the total surface area of the hemisphere where the radius of the hemisphere is $10cm$. Let us consider the figure below,

We know that the total surface area of the hemisphere = curved surface area + base area.
We also know that the curved surface area of the hemisphere $=2\pi {{r}^{2}}$. The base of the hemisphere is circular, therefore, the base area of hemisphere $=\pi {{r}^{2}}$.
Therefore, the total surface area of the hemisphere is $=3\pi {{r}^{2}}$.
Now, we can put the value of $r=10$ in the formula $3\pi {{r}^{2}}$ to get the total surface area of the hemisphere. So, we get,
$3\pi {{r}^{2}}=3\pi {{\left( 10 \right)}^{2}}$
$\Rightarrow 3\pi \left( 100 \right)$
Taking the value of $\pi =3.14$ in the above equation we get:
$\Rightarrow 3\times 3.14\times 100$
$=942$
As we know that the area is given in terms of $sq.units$, therefore, the total surface area of the given hemisphere is $942sq.units$.
Note: In the question, the total surface area of the hemisphere has been asked, so we must not forget to add the base area of the hemisphere to the curved surface area of the hemisphere. This is the probable mistake that can be committed while solving this question. We can also take the value of $\pi =\dfrac{22}{7}$.