Question

Find the volume and surface area of a sphere of radius 6.3 cm.

Answer 1

Hint: Hint: In this question, we are given a sphere whose radius is 6.3 cm. We have to find the volume and surface area of the given sphere. We will use the formula for finding the surface area of the sphere given by $A=4\pi {{r}^{2}}$ where A is surface area and r is the radius of the sphere. We will use the formula for finding the volume of the sphere given by $V=\dfrac{4}{3}\pi {{r}^{3}}$ where V is the volume of sphere and r is the radius of the sphere.

Complete step by step answer:
Here we are given a sphere with radius 6.3 cm. We have to find the surface area of the sphere first.
As we know, surface area of a solid object is a measure of the total area that the surface of the object occupies. The formula for finding surface area of the sphere is given by $A=4\pi {{r}^{2}}$.
Radius of the sphere is given as 6.3 cm
Therefore, r = 6.3 cm
Hence, surface area of sphere \[\Rightarrow 4\times \pi \times {{\left( 6.3 \right)}^{2}}\]
As we know, $\pi =\dfrac{22}{7}$
Therefore, \[A=4\times \dfrac{22}{7}\times 6.3\times 6.3\]
For solving decimal numbers, let’s remove decimal by dividing the number by 10.
\[\begin{align}
  & A=4\times \dfrac{22}{7}\times \dfrac{63}{10}\times \dfrac{63}{10} \\
 &\Rightarrow A=498.96c{{m}^{2}} \\
\end{align}\]
Hence, surface area of given sphere is $498.96c{{m}^{2}}$
Now, let us find the volume of the sphere.
Volume is the amount of sphere in a certain 3D object.
Volume of the sphere is given by $V=\dfrac{4}{3}\pi {{r}^{3}}$ where V is the volume of the sphere and r is the radius of the sphere.
Radius of sphere is given as 6.3 cm
Therefore, r = 6.3 cm
Hence, volume of sphere \[\Rightarrow \dfrac{4}{3}\pi {{r}^{3}}=\dfrac{4}{3}\times \pi \times {{\left( 6.3 \right)}^{3}}\]
As we know, $\pi =\dfrac{22}{7}$
Therefore, \[V=\dfrac{4}{3}\times \dfrac{22}{7}\times 6.3\times 6.3\times 6.3\]
For solving decimal numbers, let’s remove decimal by dividing the number by 10.
\[\begin{align}
  & V=\dfrac{4}{3}\times \dfrac{22}{7}\times \dfrac{63}{10}\times \dfrac{63}{10}\times \dfrac{63}{10} \\
 &\Rightarrow V=1047.817c{{m}^{3}} \\
\end{align}\]
Hence, volume of given sphere is $1047.817c{{m}^{3}}$

Thus, radius of given sphere is $498.96c{{m}^{2}}$ and volume of given sphere is $1047.817c{{m}^{3}}$

Note: Students should not forget to put units for radius, surface area and volume. For radius we use cm, for surface area we use $c{{m}^{2}}$ and for volume we use $c{{m}^{3}}$. Students should always remember the formula for finding surface area and volume of all three dimensional objects. Students should know that, for a sphere to have only normal surface area neither total surface area nor lateral surface area. Almost all other 3D objects have two types of surface areas.