The density of osmium (the densest metal) is 22.57 g/ cm3. If a 1.00 kg rectangular block of osmium has two dimensions of 4.00 cm x 4.00 cm, calculate the third dimension of the block.
density = mass/volume, so
1000g / (4*4*x cm^3) = 22.57 g/cm^3
x = 1000/(22.57*16) = 2.769 cm
To calculate the third dimension of the block, we can use the formula for density:
Density = mass / volume.
In this case, the mass of the block is given as 1.00 kg, and the density of osmium is given as 22.57 g/cm^3. To use consistent units, we need to convert the mass from kg to g:
1.00 kg = 1000 g.
Now let's calculate the volume of the block. Since the block is a rectangular shape, its volume can be found using the formula:
Volume = length × width × height.
Two of the dimensions are given as 4.00 cm x 4.00 cm, and the third dimension is what we need to find. Let's call the third dimension "h" for height.
So, the volume can be expressed as:
Volume = 4.00 cm × 4.00 cm × h.
Now, let's substitute the given values into the formula for density:
22.57 g/cm^3 = 1000 g / (4.00 cm × 4.00 cm × h).
To solve for h, we need to isolate it on one side of the equation. First, divide both sides of the equation by 1000 g:
(22.57 g/cm^3) / (1000 g) = 1 / (4.00 cm × 4.00 cm × h).
Now, rearrange the equation to solve for h:
h = 1 / ((22.57 g/cm^3) / (1000 g × 4.00 cm × 4.00 cm)).
Simplifying the expression further gives:
h = 1 / (22.57 g / (1000 g × 16.00 cm^2)).
h = (1000 g × 16.00 cm^2) / 22.57 g.
h = 64000 cm^2 / 22.57 g.
Finally, we can perform the division to find the value of h:
h ≈ 2837.77 cm^2/g.
Therefore, the third dimension of the osmium block is approximately 2837.77 cm^2/g.
To calculate the third dimension of the osmium block, we can use the formula for density:
Density = Mass / Volume
Given that the mass of the block is 1.00 kg and the two dimensions are 4.00 cm x 4.00 cm, let's denote the third dimension as "d".
First, let's calculate the volume of the osmium block using the given dimensions:
Volume = length x width x height
Since the length and width are both 4.00 cm, we can substitute these values into the formula:
Volume = 4.00 cm x 4.00 cm x d
Now, let's substitute the known values and rearrange the formula to solve for "d":
Density = Mass / Volume
22.57 g/cm^3 = 1.00 kg / (4.00 cm x 4.00 cm x d)
To get the volume in cubic centimeters, we need to convert the mass from kg to g:
1.00 kg = 1000 g
Substituting the values into the formula:
22.57 g/cm^3 = 1000 g / (4.00 cm x 4.00 cm x d)
Rearranging the formula to solve for "d":
d = 1000 g / (22.57 g/cm^3 x 4.00 cm x 4.00 cm)
Evaluating the expression:
d = 1000 / (22.57 x 4.00 x 4.00)
d ≈ 2.26 cm
Therefore, the third dimension of the osmium block is approximately 2.26 cm.