Question

The TSA of the sphere is $616c{{m}^{2}}$. Find its volume.

Answer 1

Hint: We will be using the concept of surface area and volume to solve the problem. We will first find the radius of the sphere from the total surface area of the sphere and then use the formula of volume of sphere to find its volume.
Complete step-by-step answer:
Now, we have been given that the total surface area of the sphere is $616c{{m}^{2}}$.
Now, we know that for a sphere of radius r the total surface area is $4\pi {{r}^{2}}$.

Now, according to question we have,
$\begin{align}
  & 4\pi {{r}^{2}}=616 \\
 & \pi {{r}^{2}}=\dfrac{616}{4} \\
 & \pi {{r}^{2}}=154 \\
\end{align}$
Now, we will use $\pi =\dfrac{22}{7}$. So,
$\begin{align}
  & \dfrac{22}{7}{{r}^{2}}=154 \\
 & {{r}^{2}}=\dfrac{154\times 7}{22} \\
 & {{r}^{2}}=\dfrac{77\times 7}{11} \\
 & {{r}^{2}}=7\times 7 \\
 & r=7cm \\
\end{align}$
Now, we have to find the volume of sphere and we know that the formula for volume of sphere is
\[=\dfrac{4}{3}\pi {{r}^{3}}\].
Now, we will substitute the value of r = 7 and $\pi =\dfrac{22}{7}$. So, we have the volume of sphere as,
$\begin{align}
  & =\dfrac{4}{3}\times \dfrac{22}{7}\times 7\times 7\times 7 \\
 & =\dfrac{4}{3}\times 22\times 7\times 7 \\
 & =\dfrac{4312}{3} \\
 & =1437.33c{{m}^{3}} \\
\end{align}$
The volume of the sphere is $1437.33c{{m}^{3}}$.

Note: To solve these type of questions it is important to know that the total surface area of a sphere of radius r is $4\pi {{r}^{2}}$ and volume of such sphere is \[\dfrac{4}{3}\pi {{r}^{3}}\]. Also, it has to be noted the way we have used total surface area to find the radius of the sphere.