1. A piece of rectangular wood that measures 3.0 cm by 6.0 cm by 4.0 cm has a mass of 80.0 grams. What is the density of the wood? Would the piece of wood float in water?
2. I threw a plastic ball in the pool for my dog to fetch. The mass of the ball was 125g. What must the volume be to have a density of 0.500 g/mL?
#1.
Recall that the density of a material is just
d = m/V
where:
m = mass
V = volume
Also, the volume of a rectangular solid is given by
V = l*w*h
where:
l = length
w = width
h = height
Substituting,
d = 80 / (3*6*4)
d = 80 / 72
d = 1.11 g / cm^3
No, it will NOT float because the density of wood is greater than density of water (which is approximately 1 g /cm^3 at standard temperature & pressure)
#2.
d = m/V
V = m/d
V = 125 / 0.5
V = 250 mL
Hope this helps~ :)
it helped :D
1. To find the density of the wood, you can use the formula:
Density = Mass / Volume
Given:
Mass = 80.0 grams
To find the volume of the wood, you need to multiply its dimensions:
Volume = Length x Width x Height
= 3.0 cm x 6.0 cm x 4.0 cm
= 72.0 cm³
Now, substitute the values into the formula:
Density = 80.0 g / 72.0 cm³
Density ≈ 1.11 g/cm³
Since the density of water is approximately 1 g/cm³, the wood with a density of 1.11 g/cm³ is more dense than water. Therefore, the piece of wood would sink in water rather than float.
2. To find the volume of the plastic ball with a density of 0.500 g/mL, you can rearrange the density formula:
Volume = Mass / Density
Given:
Mass = 125 g
Density = 0.500 g/mL
First, convert the density from grams per milliliter to grams per cubic centimeter (g/mL to g/cm³) since volume is typically expressed in cubic centimeters:
Density = 0.500 g/mL x 1 mL / 1 cm³
= 0.500 g/cm³
Now, substitute the values into the formula:
Volume = 125 g / 0.500 g/cm³
Volume ≈ 250 cm³
So, the volume of the plastic ball must be approximately 250 cm³ in order to have a density of 0.500 g/mL.
To find the density of an object, you need to divide the mass of the object by its volume.
1. Density of the wood:
Given dimensions: Length = 6.0 cm, Width = 3.0 cm, Height = 4.0 cm
Volume of the wood = Length × Width × Height = 6.0 cm × 3.0 cm × 4.0 cm = 72.0 cm³
Density = Mass / Volume = 80.0 g / 72.0 cm³ = 1.11 g/cm³
To determine if the wood will float in water, we compare the density of the wood with the density of water, which is 1.0 g/cm³. Since the density of the wood (1.11 g/cm³) is greater than the density of water, the piece of wood will sink in water.
2. Volume of the plastic ball:
Density = Mass / Volume
Rearranging the equation, Volume = Mass / Density
Given density = 0.500 g/mL and mass = 125 g:
Volume = 125 g / 0.500 g/mL = 250 mL
Therefore, the volume of the plastic ball must be 250 mL to have a density of 0.500 g/mL.