a solid alumimium casting for a pulley consists of the discs each 1 1/2 cm thick of diameters 4 cm, 6 cm,and 8 cm.a central hole 2 cm in diameter is drilled out .if the density of the alumimium is 2.8g/cm^3,calculate the mass of the casting
I see a volume of
π(2^2)(1.5) + π(3^2)(1.5) + π(4^2)(1.5) - π(1^2)(4.5)
then multiply that result by 2.8 to get the mass in grams
Soive it for me i don't want hint
I do not understand
Pls where did you get your 4.5 from. I dont get
The 4.5
There are 3 disks each is 1.5 cm thick so the total of the three is 1.5 multiplied by 3
Why did the pulley go on a diet? It wanted to be light as aluminum!
To calculate the mass of the casting, we need to determine the volume of aluminum used and then multiply it by the density.
First, let's calculate the volume of the aluminum used:
For the 4 cm diameter disc:
Radius = diameter/2 = 4 cm/2 = 2 cm
Volume = π * r^2 * h = π * (2 cm)^2 * (1 1/2 cm) = π * 4 cm^2 * 1.5 cm
For the 6 cm diameter disc:
Radius = diameter/2 = 6 cm/2 = 3 cm
Volume = π * r^2 * h = π * (3 cm)^2 * (1 1/2 cm) = π * 9 cm^2 * 1.5 cm
For the 8 cm diameter disc:
Radius = diameter/2 = 8 cm/2 = 4 cm
Volume = π * r^2 * h = π * (4 cm)^2 * (1 1/2 cm) = π * 16 cm^2 * 1.5 cm
Now, let's calculate the volume of the central hole:
Radius = diameter/2 = 2 cm/2 = 1 cm
Volume = π * r^2 * h = π * (1 cm)^2 * (1 1/2 cm) = π * 1 cm^2 * 1.5 cm
Finally, let's calculate the total volume of the casting by subtracting the volume of the central hole from the sum of the volumes of the discs:
Total Volume = [(π * 4 cm^2 * 1.5 cm) + (π * 9 cm^2 * 1.5 cm) + (π * 16 cm^2 * 1.5 cm)] - (π * 1 cm^2 * 1.5 cm)
Now, multiply the total volume by the density of aluminum (2.8 g/cm^3) to find the mass of the casting.
Remember, math can be a bit heavy! Let me do the calculations for you.
To calculate the mass of the aluminum casting, we need to calculate the volume of each disc and then sum them up.
First, let's calculate the volume of each disc. The volume of a disc can be calculated using the formula for the volume of a cylinder:
Volume = π * r^2 * h
where π is a constant approximately equal to 3.14159, r is the radius of the disc, and h is the thickness of the disc.
For the first disc with a diameter of 4 cm and a thickness of 1 1/2 cm (or 1.5 cm), the radius (r) can be calculated as half of the diameter:
r = 4 cm / 2 = 2 cm
Now we can calculate the volume of the first disc:
Volume1 = π * (2 cm)^2 * 1.5 cm
Repeat the same process for the other two discs:
For the second disc with a diameter of 6 cm and a thickness of 1 1/2 cm (or 1.5 cm):
r = 6 cm / 2 = 3 cm
Volume2 = π * (3 cm)^2 * 1.5 cm
For the third disc with a diameter of 8 cm and a thickness of 1 1/2 cm (or 1.5 cm):
r = 8 cm / 2 = 4 cm
Volume3 = π * (4 cm)^2 * 1.5 cm
Now that we have the volumes of each disc, we can calculate the total volume of the casting by summing up the volumes:
Total Volume = Volume1 + Volume2 + Volume3
Next, we can use the density of aluminum and the total volume to calculate the mass of the casting. The formula to calculate the mass is:
Mass = Density * Volume
In this case, the density of aluminium is given as 2.8 g/cm^3. So we can substitute the value of density and total volume into the formula to calculate the mass of the casting:
Mass = 2.8 g/cm^3 * Total Volume
Finally, calculate the value of Mass to get your answer.
Note: Make sure to convert cm to cm^3 throughout the calculations to maintain consistent units.