The height of a cylindrical container is 15 cm and the inside diameter of the container is 10 cm.
a) what is the volume?
b) How much weight (in kg) would be required to fill the container to a density of 1.3 g/cm^3?
V = pi (5)^2 * 15
m/V = 1.3
so in grams m = 1.3 V
divide by 1000 to get kg
a) To find the volume of a cylindrical container, you can use the formula:
Volume = π * r^2 * h
Where:
π is a mathematical constant approximately equal to 3.14159
r is the radius of the cylinder (half of the diameter)
h is the height of the cylinder
In this case, the inside diameter is given as 10 cm. So, we can find the radius by dividing the diameter by 2:
Radius = 10 cm / 2 = 5 cm
The height is given as 15 cm. Now we can substitute these values into the formula:
Volume = 3.14159 * (5 cm)^2 * 15 cm
Simplifying the calculation, we have:
Volume = 3.14159 * 25 cm^2 * 15 cm
Volume = 1178.0975 cm^3
Therefore, the volume of the cylindrical container is 1178.0975 cm^3.
b) To find the weight of a substance, you can use the formula:
Weight = Volume * Density
Where:
Volume is the volume of the substance
Density is the density of the substance
In this case, the given density is 1.3 g/cm^3. However, we need the density in kg/cm^3. To convert grams (g) to kilograms (kg), divide the value by 1000:
Density = 1.3 g/cm^3 = 1.3 kg / 1000 cm^3
Now, we have the volume:
Volume = 1178.0975 cm^3
Substituting the values into the formula, we can calculate the weight:
Weight = 1178.0975 cm^3 * (1.3 kg / 1000 cm^3)
Simplifying the calculation, we have:
Weight = 1.53152 kg
Therefore, to fill the cylindrical container with a density of 1.3 g/cm^3, it would require a weight of 1.53152 kg.