To find the volume [tex]\( V \)[/tex] of a sphere, we use the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Where:
- [tex]\( V \)[/tex] is the volume of the sphere.
- [tex]\( r \)[/tex] is the radius of the sphere.
- [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14159.
In our example, the radius [tex]\( r \)[/tex] is given as 1 inch. Let's substitute the radius into the formula:
[tex]\[ V = \frac{4}{3} \pi (1)^3 \][/tex]
Calculating the power first:
[tex]\[ (1)^3 = 1 \][/tex]
Now the formula simplifies to:
[tex]\[ V = \frac{4}{3} \pi \times 1 \][/tex]
Since [tex]\(\pi\)[/tex] is approximately 3.14159, we can substitute this value in:
[tex]\[ V = \frac{4}{3} \times 3.14159 \][/tex]
Performing the multiplication and division:
[tex]\[ V = 4.18879 \, \text{in}^3 \][/tex]
Therefore, the volume of the sphere with a radius of 1 inch is approximately [tex]\( 4.18879 \, \text{in}^3 \)[/tex].
