Calculate the density of a substance in pennyweights that has a volume of 0.287hogsheads and a mass of 55.25kg.
1 pennyweight= 1.55g
1 hogshead=238.5 liters
1 peck=9.091 liters
Answer in pw/pk.
I assume pw/pk = pennyweight/peck.
55250 x (1 pw/1.55g) = ?mass in pw.
0.287 hh x (238.5 L/1 hh) x (1 pk/9.091 L) = ?volume in pecks.
Then density = ?pw/?pk. Substitute and solve.
To calculate the density of the substance in pennyweights per peck, we need to convert the given volume and mass to the appropriate units.
Step 1: Convert the given volume from hogsheads to liters:
Since 1 hogshead is equal to 238.5 liters, we can calculate the volume in liters by multiplying 0.287 hogsheads by 238.5 liters/hogshead:
Volume = 0.287 hogsheads * 238.5 liters/hogshead = 68.5595 liters
Step 2: Convert the given mass from kilograms to grams:
Since 1 kilogram is equal to 1000 grams, we can calculate the mass in grams by multiplying 55.25 kg by 1000 g/kg:
Mass = 55.25 kg * 1000 g/kg = 55250 grams
Step 3: Calculate the density:
Density is defined as the mass divided by the volume. However, we need to adjust the units to meet the desired result (pennyweights per peck).
1 peck is equal to 9.091 liters.
1 pennyweight is equal to 1.55 grams.
So, to calculate the density in pennyweights per peck, we can use the following formula:
Density = (Mass in grams * (1 pennyweight/1.55 grams)) / (Volume in liters * (1 peck/9.091 liters))
Now, let's substitute the values into the formula:
Density = (55250 g * (1 pw/1.55 g)) / (68.5595 L * (1 pk/9.091 L))
Simplifying further:
Density = (55250/1.55) pw / (68.5595/9.091) pk
Finally, calculate the density:
Density ≈ 35687.0968 pw/pk
Therefore, the density of the substance is approximately 35687.0968 pennyweights per peck.