Nuclear waste material in a physics lab is stored in a cylinder of height 4.81 inch and circumference of 8.18 in. What is the volume of the cylinder in metric unit?

1685997.4 mm³ or 1685.9974 cm³

Explanation:

The most common unit that is used to measure length in the metric system is millimeter (mm).

The volume of a cylinder = Area of the circular base*height.

V = πr²h ... Equation 1

Where V = volume of the nuclear waste material, r = radius of the cylinder, h = height of the cylinder.

But circumference of a circle,

P = 2πr

r = P/2π

Where p = circumference of the circle = 8.18 in and π = 3.14.

r = 8.18 / (2*3.14)

r = 1.3 in

Given: h = 4.81 inch, r = 1.3 inch.

Conversion: From Inch to mm

(i) if, 1 inch = 25.4 mm,

Then 4.81 inch = 25.4 (4.81) = 122.174 mm

(ii) if, 1 inch = 25.4 mm,

Then, 1.3 inch = 25.4 (1.3) = 33.02 mm.

Therefore, h = 122.174, r = 33.02 mm

Substituting these values into equation Equation

V = 3.14 (33.02) ²122.174

v = 384039.59 mm³ or 384.0395 cm³

Thus the volume of the cylinder = 384039.59 mm³ or 384.0395 cm³