Question

problem 2
draw a cylinder with a diameter of 6 centimeters and a volume of 36π cubic centimeters.
here is the cylinder you sketched on the previous screen.
determine the radius and the height of the cylinder.
radius (cm) 3
height (cm)
show or explain your thinking.
then label your drawing with the cylinder’s radius and height.

Explanation:

Step1: Recall the volume formula of a cylinder

The volume \( V \) of a cylinder is given by the formula \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. We know that the diameter \( d = 6\) cm, so the radius \( r=\frac{d}{2}=\frac{6}{2} = 3\) cm (which is also given in the table), and the volume \( V = 36\pi\) cubic centimeters.

Step2: Substitute the known values into the formula and solve for \( h \)

Substitute \( V = 36\pi\) and \( r = 3\) into the formula \( V=\pi r^{2}h \):
\[
36\pi=\pi\times(3)^{2}\times h
\]
Simplify the right - hand side: \( \pi\times9\times h=9\pi h \)
So the equation becomes \( 36\pi = 9\pi h \)
Divide both sides of the equation by \( 9\pi \) (since \( \pi
eq0 \)):
\[
h=\frac{36\pi}{9\pi}=4
\]

Answer:

The height of the cylinder is \( 4 \) cm. So in the table, the value under the "Height (cm)" column should be \( 4 \).