Sure! Let’s walk through the process of determining the volume of a cylinder with the given dimensions.
The formula for finding the volume [tex]\( V \)[/tex] of a cylinder is:
[tex]\[ V = \pi r^2 h \][/tex]
Where:
- [tex]\( \pi \)[/tex] (pi) is a constant approximately equal to 3.14159
- [tex]\( r \)[/tex] is the radius of the base of the cylinder
- [tex]\( h \)[/tex] is the height of the cylinder
Here, the provided details are:
- Radius [tex]\( r = 8 \)[/tex] cm
- Height [tex]\( h = 7 \)[/tex] cm
To find the volume:
1. Substitute the known values into the formula:
[tex]\[ V = \pi (8^2) (7) \][/tex]
2. Calculate the square of the radius:
[tex]\[ 8^2 = 64 \][/tex]
3. Multiply this result by the height:
[tex]\[ 64 \times 7 = 448 \][/tex]
4. Multiply this product by [tex]\( \pi \)[/tex]:
[tex]\[ V = \pi \times 448 \][/tex]
5. Using the value of [tex]\( \pi \)[/tex]:
[tex]\[ V \approx 3.14159 \times 448 \][/tex]
[tex]\[ V \approx 1407.4335088082273 \][/tex]
Thus, the volume of the cylinder is approximately 1407.4335088082273 cubic centimeters.
Finally, rounding this value to the nearest tenths place:
- Identify the tenths place (1 digit after the decimal point), which is 4.
- Look at the next digit, which is 3.
- Since 3 is less than 5, we do not round up.
So, the volume rounded to the nearest tenths place is:
[tex]\[ 1407.4 \][/tex]
Therefore, the volume of the cylinder is approximately [tex]\( 1407.4 \)[/tex] cubic centimeters.
