A cylinder wooden column is 3m high and 28cm in diameter.Use the value for π to calculate:
a. The volume of column.
b. The mass,in kg of the column if
the density of the wood is 0.8g/cm^3.
a. The volume of the column is calculated as follows:
radius = diameter/2 = 28cm/2 = 14cm
height = 3m = 300cm
Volume = π × radius^2 × height
Volume = π × (14cm)^2 × 300cm
Volume ≈ 185932.56 cm^3
b. The mass of the column can be calculated using the following formula:
mass = volume × density
density = 0.8 g/cm^3
mass = 185932.56 cm^3 × 0.8 g/cm^3
mass ≈ 148746.04 g
To convert grams to kilograms, we divide by 1000:
mass = 148746.04 g ÷ 1000
mass ≈ 148.75 kg
Therefore, the mass of the column is approximately 148.75 kg.
A round house is made of two basic shapes:a cylinder and a cone. Calculate the volume of air in a round house.Use the value 22÷7 for π.
We need more information in order to calculate the volume of air in the round house. Specifically, we need to know the dimensions of the cylinder and cone. Once we have those, we can calculate the volume of each shape and add them together to get the total volume of the round house.
Assuming we have the necessary information:
Let's say the round house has a cylinder with a height of 4 meters and a radius of 5 meters. The formula for the volume of a cylinder is:
V_cylinder = π × r^2 × h
where r is the radius of the cylinder, h is the height of the cylinder, and π is the constant pi.
Plugging in our values, we get:
V_cylinder = 22/7 × 5^2 × 4
V_cylinder ≈ 314.29 m^3
Now let's say the round house also has a cone with a height of 3 meters and a radius of 5 meters. The formula for the volume of a cone is:
V_cone = 1/3 × π × r^2 × h
where r is the radius of the base of the cone, h is the height of the cone, and π is the constant pi.
Plugging in our values, we get:
V_cone = 1/3 × 22/7 × 5^2 × 3
V_cone ≈ 78.57 m^3
Therefore, the total volume of air in the round house is:
V_total = V_cylinder + V_cone
V_total ≈ 392.86 m^3
So the volume of air in the round house is approximately 392.86 cubic meters.
a. The volume of the cylinder can be calculated using the formula:
V = π * r^2 * h
where V is the volume, π is the mathematical constant pi, r is the radius of the cylinder, and h is the height of the cylinder.
First, let's calculate the radius of the cylinder. The diameter is given as 28 cm, so the radius is half of that:
r = 28 cm / 2 = 14 cm
Now, we need to convert the height from meters to centimeters:
h = 3 m * 100 cm/m = 300 cm
Substituting the values into the formula, we get:
V = π * (14 cm)^2 * 300 cm ≈ 617,763.35 cm^3
b. To calculate the mass of the column, we can use the formula:
mass = density * volume
Given that the density of the wood is 0.8 g/cm^3 and we already calculated the volume to be 617,763.35 cm^3, we can substitute the values into the formula:
mass = 0.8 g/cm^3 * 617,763.35 cm^3 = 494,210.68 g
To convert the mass from grams to kilograms, we divide by 1000:
mass = 494,210.68 g / 1000 = 494.21 kg (rounded to two decimal places)
Therefore, the mass of the column is approximately 494.21 kg.