A roll of quarters is shaped like a cylinder and contains 40 each quarter has a thickness of 1.75 and a diameter of 24.26 mm What measurement would be the closest to the volume of one roll of quarters in cubic millimeters

A) 5,335mm
B) 6,256mm
C) 129,428mm
D) 32,357mm

Respuesta :

Answer:

D) 32,357mm^3

Step-by-step explanation:

Given

[tex]Quarters = 40[/tex]

[tex]Thickness = 1.75mm[/tex]

[tex]diameter = 24.26mm[/tex]

First, we calculate the volume of 1 roll.

The volume of the cylinder is:

[tex]V = \pi r^2h[/tex]

Where

[tex]r = \frac{1}{2} * diameter[/tex]

[tex]r = \frac{1}{2} * 24.26mm[/tex]

[tex]r = 12.13mm[/tex]

And the thickness represents the height.

So:

The volume is:

[tex]V = 3.142 * 12.13^2 * 1.75[/tex]

[tex]V = 809.03mm^3[/tex]

The volume of the 40 is:

[tex]Roll= 40 * 809.03mm^3[/tex]

[tex]Roll=32361.20mm^3[/tex]

The closest option is (d):