Answer:
given that a right circular cylinder is 12 full of water, volume of water in the container is 36 cubic inches and the height of the container is 9 inches.
We have to find the diameter of the base of the cylinder in inches.
Let us first draw the diagram of the right circular cylinder:
Let,
r be the radius of the cylinder.
Since the container of a right circular cylinder is 12 full of water and height of the container is 9 inches then height of the water is =9(12)=4.5
Now, use the formula of volume of the right circular cylinder.
Volume of the cylinder=πr2(height)
Substitute 36 for volume and 4.5 for height in above equation.
⇒36=πr2(4.5)
Divide each side by 4.5
⇒8=πr2
Divide each side by π
⇒8π=r2
Take the square root on each side.
⇒8π=−−−−√r2−−√⇒8π−−√=r
Simplify further.
⇒r=22π−−√
Therefore, the radius of the cylinder is r=22π−−√ inches.
Since, the diameter is twice the length of the radius.
Thus, the diameter of the base of the cylinder=2r=2(22π−−√)=42π−−√ inches
