Sure! Let's work through this step-by-step.
The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the cylinder's base,
- [tex]\( h \)[/tex] is the height of the cylinder,
- [tex]\( \pi \)[/tex] (pi) is a mathematical constant approximately equal to 3.14159.
Let's say we have a cylinder with a radius [tex]\( r \)[/tex] of 5 units and a height [tex]\( h \)[/tex] of 10 units. To find the volume of this cylinder, we will substitute these values into the formula.
1. Substitute the radius and height into the formula:
[tex]\[ V = \pi (5)^2 (10) \][/tex]
2. Calculate the square of the radius:
[tex]\[ (5)^2 = 25 \][/tex]
3. Substitute this result back into the formula:
[tex]\[ V = \pi \times 25 \times 10 \][/tex]
4. Multiply 25 by 10:
[tex]\[ 25 \times 10 = 250 \][/tex]
5. Now multiply by [tex]\( \pi \)[/tex]:
[tex]\[ V = \pi \times 250 \][/tex]
6. Using the approximate value of [tex]\( \pi \)[/tex] (3.14159):
[tex]\[ V \approx 3.14159 \times 250 \][/tex]
7. Calculate the final result:
[tex]\[ V \approx 785.3981633974483 \][/tex]
Therefore, the volume of the cylinder with a radius of 5 units and a height of 10 units is approximately 785.398 cubic units.
