Answer:
diameter = 18 mm
Step-by-step explanation:
We can find the diameter of a cylinder with volume 3306.42 mm³ and height 13 mm by finding its radius using the Cylinder Volume Formula:
[tex]\boxed{V=\pi r^2h}[/tex]
where:
[tex]V=\pi r^2h[/tex]
[tex]3306.42=3.14\times r^2\times13[/tex]
[tex]\displaystyle r^2=\frac{3306.42}{3.14\times13}[/tex]
[tex]r=\sqrt{81}[/tex]
[tex]\bf r=9\ mm[/tex]
[tex]\boxed{diameter = 2\times radius}[/tex]
[tex]diameter=2\times9[/tex]
[tex]\bf diameter=18\ mm[/tex]
First, use the formula for the volume of a sphere and solve for the radius.
Formula: [tex]V=\pi r^{2}h[/tex]
Substitute known values: [tex]3306.42=\pi r^{2}\cdot13[/tex]
Divide by 13 pi. [tex]\frac{3306.42}{13\pi}=r^{2}[/tex], [tex]r^{2}=\frac{3306.42}{13\pi}[/tex]
Take the square root: [tex]r=\sqrt{\frac{3306.42}{13\pi}}[/tex]= 8.99
The radius is half the diameter, so the diameter is 2 * 8.99 = 17.99.
So, the final answer is 18mm round to the nearest whole number.
