The density of osmium is 22.57g/cm3. If a 1.00kg rectangular block of osmium has two dimensions of 4.00cmx4.00cm, calculate the third dimension of the block.
Ah, the third dimension, it's always the mysterious one, isn't it? Well, let's solve this riddle together! We know that the mass of the osmium block is 1.00 kg, and its density is 22.57 g/cm3. Since density is defined as mass divided by volume, we can find the volume of the block by dividing the mass by the density.
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!
To solve this problem, we need to use the formula for density:
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.
To find the third dimension of the rectangular block of osmium, we can use the formula for density, which relates mass, volume, and density.
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.
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.