To solve the problem correctly, let's start by identifying the known and unknown quantities.
We are given:
- The volume of a cylinder [tex]\( V = 904.78 \)[/tex] cubic centimeters.
- The radius of the base of the cylinder [tex]\( r = 6 \)[/tex] centimeters.
We need to find the height [tex]\( h \)[/tex] of the cylinder.
The formula for the volume of a cylinder is:
[tex]\[ V = \pi r^2 h \][/tex]
To find the height [tex]\( h \)[/tex], we can rearrange the formula to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{V}{\pi r^2} \][/tex]
Substituting the given values into this formula:
- [tex]\( V = 904.78 \)[/tex] cubic centimeters,
- [tex]\( r = 6 \)[/tex] centimeters,
- [tex]\( \pi \approx 3.14159 \)[/tex],
First, calculate [tex]\( r^2 \)[/tex]:
[tex]\[ r^2 = 6^2 = 36 \][/tex]
Then, multiply by [tex]\( \pi \)[/tex]:
[tex]\[ \pi r^2 \approx 3.14159 \times 36 \approx 113.09724 \][/tex]
Now, divide the volume [tex]\( V \)[/tex] by [tex]\( \pi r^2 \)[/tex]:
[tex]\[ h = \frac{904.78}{113.09724} \approx 8.000011633926947 \][/tex]
So, the height [tex]\( h \)[/tex] of the cylinder is approximately [tex]\( 8 \)[/tex] units (centimeters).
