mass = volume x density
mass in grams, volume in cc and density in g/cc.
You have mass (1000 g) and density (22.57 g/cc). Calculate volume. Then remember volume = length x width x height. You have length and width, calculate height.
mass in grams, volume in cc and density in g/cc.
You have mass (1000 g) and density (22.57 g/cc). Calculate volume. Then remember volume = length x width x height. You have length and width, calculate height.
So, the volume of the block is:
Volume = mass/density
Volume = 1000 g / 22.57 g/cm3
Volume = 44.27 cm3
Now, we know that the block has two dimensions of 4.00 cm x 4.00 cm. Let's call the third dimension "x".
So, the volume of the block can also be calculated by multiplying the three dimensions:
Volume = 4.00 cm x 4.00 cm x x cm
Now, we just need to solve for "x" by equating the two volumes:
4.00 cm x 4.00 cm x x cm = 44.27 cm3
Solving for "x" gives us:
x = 44.27 cm3 / (4.00 cm x 4.00 cm)
x = 2.77 cm
So, the third dimension of the osmium block is 2.77 cm. Voila! Mystery solved!
Density = mass / volume
Given that the density of osmium is 22.57 g/cm^3, and the mass of the osmium block is 1.00 kg, we can rearrange the formula to solve for volume:
Volume = mass / density
Volume = 1000 g / 22.57 g/cm^3
Next, we need to determine the volume of the rectangular block. The volume of a rectangular block can be calculated by multiplying the length, width, and height. We know that two of the dimensions are 4.00 cm x 4.00 cm, so we need to find the third dimension (height).
Volume = length x width x height
We can substitute the volume value calculated earlier into this equation:
1000 g / 22.57 g/cm^3 = (4.00 cm) x (4.00 cm) x height
To find the value of height, we need to divide both sides of the equation by (4.00 cm) x (4.00 cm):
height = (1000 g / 22.57 g/cm^3) / (4.00 cm x 4.00 cm)
height = 5.53 cm
So, the third dimension of the osmium block is 5.53 cm.
Density = Mass / Volume
We are given the density of osmium as 22.57 g/cm³ and the mass of the block as 1.00 kg. We can first convert the mass to grams:
Mass = 1.00 kg * 1000 g/kg = 1000 g
Since the block is rectangular, we can calculate its volume by multiplying the three dimensions together:
Volume = Length x Width x Height
We are given two of the dimensions: 4.00 cm and 4.00 cm. Let's call the third dimension as "h" cm.
Plugging in the given values, we have:
22.57 g/cm³ = 1000 g / (4.00 cm x 4.00 cm x h cm)
Now we can isolate the third dimension "h" by rearranging the equation:
h cm = 1000 g / (22.57 g/cm³ x 4.00 cm x 4.00 cm)
Calculating this expression, we get:
h cm ≈ 2.198 cm
Therefore, the third dimension of the rectangular block of osmium is approximately 2.198 cm.