Calculate the mass of a cylindrical cork of diameter 1.00 inches and length 2.50 inches. Pay attention to significant figures, Cork density 0.26 g/ mL
there are 2.54 cm in an inch
a cm^3 is the same as a mL
volume = π * .5^2 * 2.5 * 2.54^3
...the result is in cm^3
multiply the volume by the density (.26)...that is the mass in g
round the result to TWO sig fig
...that is the limiting number in the density value
To calculate the mass of the cylindrical cork, we first need to find the volume of the cork using its dimensions and then multiply by its density.
Step 1: Calculate the volume of the cylindrical cork.
The volume of a cylindrical object is given by the formula V = πr^2h, where r is the radius and h is the height (or length) of the cylinder.
Given:
Diameter (d) = 1.00 inches (To find the radius, divide the diameter by 2)
Length (h) = 2.50 inches
Calculations:
Radius (r) = d/2 = 1.00 inches / 2 = 0.50 inches
Converting inches to centimeters:
1 inch = 2.54 cm
0.50 inches = 0.50 * 2.54 cm = 1.27 cm
Volume of the cylinder = πr^2h = π * (1.27 cm)^2 * 2.50 cm
Note: Since we are given the density in grams per milliliter, it would be better to use the metric system to ensure consistency.
Step 2: Convert the volume to milliliters.
1 cm^3 = 1 mL
Volume = π * (1.27 cm)^2 * 2.50 cm = π * (1.27 cm)^2 * 2.50 cm = 10.01 cm^3 = 10.01 mL
Step 3: Calculate the mass of the cork.
Given Density = 0.26 g/mL
Mass = Volume * Density = 10.01 mL * 0.26 g/mL = 2.6026 g
To consider the significant figures, we should round the answer to match the least number of significant figures in the given values. In this case, the diameter (1.00 inches) has three significant figures. Therefore, the final answer should be rounded to three significant figures.
Mass = 2.6026 g (rounded to three significant figures)