Math Snap

STEP 1

Assumptions1. The density of mercury is $13.6 \mathrm{~g} / \mathrm{cm}^{3}$
. We need to find the mass in pounds of1.0 gallons of mercury3. The conversion factors are $1 \mathrm{lb}=453.6 \mathrm{~g}$ and $1 \mathrm{gal}=3.785 \mathrm{~}$

STEP 2

First, we need to convert the volume from gallons to liters.
$$Volume\, in\, liters = Volume\, in\, gallons \\times Conversion\, factor$$

STEP 3

Now, plug in the given values for the volume in gallons and the conversion factor to calculate the volume in liters.
$$Volume\, in\, liters =1.0\, gal \\times3.785\, L/gal$$

STEP 4

Calculate the volume in liters.
$$Volume\, in\, liters =1.0\, gal \\times3.785\, L/gal =3.785\, L$$

STEP 5

Next, we need to convert the volume from liters to cubic centimeters. We know that $1\, L =1000\, cm^{3}$.
$$Volume\, in\, cm^{3} = Volume\, in\, liters \\times Conversion\, factor$$

STEP 6

Now, plug in the given values for the volume in liters and the conversion factor to calculate the volume in cubic centimeters.
$$Volume\, in\, cm^{3} =3.785\, L \\times1000\, cm^{3}/$$

STEP 7

Calculate the volume in cubic centimeters.
$$Volume\, in\, cm^{3} =3.785\, L \\times1000\, cm^{3}/ =3785\, cm^{3}$$

STEP 8

Now we can calculate the mass in grams using the density of mercury.
$$Mass\, in\, grams = Volume\, in\, cm^{3} \\times Density$$

STEP 9

Now, plug in the given values for the volume in cubic centimeters and the density to calculate the mass in grams.
$$Mass\, in\, grams =3785\, cm^{3} \\times13.6\, g/cm^{3}$$

STEP 10

Calculate the mass in grams.
$$Mass\, in\, grams =3785\, cm^{3} \\times13.6\, g/cm^{3} =51516\, g$$

STEP 11

Finally, we need to convert the mass from grams to pounds.
$$Mass\, in\, pounds = Mass\, in\, grams \\times Conversion\, factor$$

STEP 12

Now, plug in the given values for the mass in grams and the conversion factor to calculate the mass in pounds.
$$Mass\, in\, pounds =51516\, g \\times\, lb/453.6\, g$$

Calculate the mass in pounds.
$$Mass\, in\, pounds =51516\, g \\times\, lb/453.6\, g =113.6\, lb$$The mass of.0 gallons of mercury is approximately113.6 pounds.