❍ Question -:
Find the volume of a sphere with a diameter of 16 cm using the formula Volume = [tex]\dfrac{4}{3}[/tex] × π × r³.
❍ Explanation -:
In this question we are provided with the diameter of a sphere. We are asked to calculate the volume of the sphere using the radius.
First we will find the radius of the sphere
We know,
[tex] ✭ \: \small\boxed{ \rm{ Radius = \dfrac{Diameter}{2}}}[/tex]
Substituting the values we get
[tex] \small\sf{ Radius = \dfrac{ \cancel{16} \: \: 8}{ \cancel{2}}}[/tex]
[tex] \star \: \small\rm{ Radius = 8 \: cm}[/tex]
Now we will calculate the volume of the sphere
We know,
[tex] ✭ \: \small \boxed{{\rm{ Volume_{(sphere)} = \dfrac{4}{3} × π × r³}}}[/tex]
Where,
- r stand for radius
- Assuming π as 3.14
Substituting the values we get
[tex] \small\rm{ Volume_{(sphere)} = \dfrac{4}{3} × 3.14 × 8³}[/tex]
[tex]\small\rm{ Volume_{(sphere)} = \dfrac{ \cancel{4}}{3} × 3.14 × 8 \times 8 \times \cancel{ 8 } \: \: 2}[/tex]
[tex] \small\rm {V olume_{(sphere)} = \dfrac{3.14 × 64}{3}}[/tex]
[tex] \small\rm{ Volume_{(sphere)} = \dfrac{200.96}{3} =66.98 \: {cm}^{3} }[/tex]
Hence the volume of the sphere is 66.98 cm³.
[tex] \underline{\rule{71mm}{4pt}}[/tex]
