a block of metal has a volume of 13.4in^3 and a weight of 5.14 lb. what is its density in grams per cm^3? Show operation
1 in^3 = 16.38 cc
13.4 in^3 to cc = ?
1 lb = 453.59 grams
5.14 lb to grams = ?
Then d = mass/volume
Well, let's see. To find the density, we need to divide the weight of the block by its volume. Now, before we start with the math, let me tell you a little joke:
Why did the scarecrow win an award?
Because he was outstanding in his field!
Alright, now let's get back to the problem. We have the weight of the block, which is 5.14 lb, and its volume, which is 13.4 in^3. To convert the weight to grams, we need to multiply it by a conversion factor of 453.592 grams per pound. To convert the volume to cm^3, we need to multiply it by a conversion factor of 16.3871 cm^3 per in^3.
So, the density can be calculated as follows:
Density = (weight in grams) / (volume in cm^3)
= (5.14 lb) * (453.592 g/lb) / (13.4 in^3) * (16.3871 cm^3/in^3)
Now, let me tell you another joke while you calculate that:
Why don't skeletons fight each other?
They don't have the guts!
Alright, did you get the answer?
To find the density of the metal block in grams per cm³, we need to use the formula:
Density = Mass / Volume
Given:
Volume = 13.4 in³
Weight = 5.14 lb
First, we need to convert the given weight from pounds (lb) to grams (g). To do this, we use the conversion factor:
1 lb = 453.592 g
So, 5.14 lb = 5.14 * 453.592 g = 2329.56488 g (rounded to 5 decimal places).
Next, we need to convert the given volume from cubic inches (in³) to cubic centimeters (cm³). To do this, we use the conversion factor:
1 in³ = 16.3871 cm³
So, 13.4 in³ = 13.4 * 16.3871 cm³ = 219.17994 cm³ (rounded to 5 decimal places).
Now that we have the mass in grams and the volume in cm³, we can calculate the density:
Density = Mass / Volume
Density = 2329.56488 g / 219.17994 cm³
Dividing these two values, we get:
Density ≈ 10.62879 g/cm³ (rounded to 5 decimal places)
Therefore, the density of the metal block is approximately 10.62879 grams per cm³.