Answer:
Solutions below.
Step-by-step explanation:
Lets define the required formulas for the question regarding the cylinder.
The base of the cylinder is a circle, therefore the formula for the circumference of the base is:
[tex]2\pi r[/tex]
The formula for the volume of the cylinder is:
[tex]\pi r^{2} h[/tex]
a) Given from the question, the circumference of the base is [tex]10\pi[/tex] mm.
Therefore, we can use the circumference formula to find radius of the base.
[tex]2\pi r = 10\pi \\2r = 10\\r = \frac{10}{2} \\r = 5mm[/tex]
b) With all the parameters given, we can find the volume of the cylinder.
Volume of the Cylinder =
[tex]\pi r^{2} h\\= \pi (5)^{2} (4)\\= 100\pi mm^{3} \\= 314.2mm^{3} (nearest\ tenth)[/tex]
