A nozzle which is attached to the end of a 4-in fire hose has a length of 1 ft and a diameter at the discharge end of 1 in. If it has a uniform thickness of 5/16 in and is made of brass, find the weight of material used in the manufacture of 1000 such nozzles. (Brass weighs 520 lb per cu. ft)
please help me how to solve this. i really don't know how. thanks in advance!
you know that weight is volume * density. You know the density, so what is the volume of brass?
\It appears we are dealing with the frustrum of a cone, narrowing from 4" to 1", with a thickness of 5/16 in. Theus, the outside diameter goes from 4.3125" to 1.3125"
Now just figure the volume of the larger shape less the volume of the inner cone, and that is the volume of brass.
Then you can get its weight, and multiply that by 1000.
The only hard part is figuring the volume of a frustrum of a cone. Google is your friend.
4709.05 lb.
To find the weight of material used in the manufacture of 1000 such nozzles, we need to calculate the volume of material used and then multiply it by the weight of brass per cubic foot.
First, let's calculate the volume of one nozzle:
1. Calculate the inner radius of the nozzle at the discharge end:
r_inner = (diameter_of_nozzle / 2) = (1 in / 2) = 0.5 in
2. Calculate the outer radius of the nozzle at the discharge end:
r_outer = r_inner + nozzle_thickness = 0.5 in + (5/16) in = (21/16) in
3. Calculate the length of the nozzle in feet:
length_nozzle_ft = 1 ft
Now, we can calculate the volume of one nozzle using the formula for the volume of a cylindrical shell:
Volume_nozzle = π * (r_outer^2 - r_inner^2) * length_nozzle_ft
Next, we will calculate the total volume of material used for 1000 nozzles:
Total_volume_material = Volume_nozzle * 1000
Finally, we can calculate the weight of the material used by multiplying the total volume of material by the weight of brass per cubic foot:
Weight_material = Total_volume_material * Weight_of_brass_per_cubic_ft
Substituting the given value for the weight of brass per cubic foot (520 lb/cu.ft), we get:
Weight_material = Total_volume_material * 520 lb/cu.ft
Now we can proceed to the calculation steps.
To solve this problem, we need to first calculate the volume of material used in manufacturing one nozzle and then multiply it by 1000 to find the total weight of material used in manufacturing 1000 nozzles.
Step 1: Calculate the volume of material used in manufacturing one nozzle.
The nozzle consists of a cylindrical part with a length of 1 ft and a diameter of 1 inch at the discharge end. We can calculate the inner and outer radii of this cylindrical part as follows:
Inner radius = (1 inch - 5/16 inch) / 2 = 11/32 inch
Outer radius = (1 inch + 5/16 inch) / 2 = 17/32 inch
Now, let's calculate the volume of the cylindrical part:
Volume of the cylindrical part = π * (Outer radius^2 - Inner radius^2) * Length
= π * [(17/32)^2 - (11/32)^2] * 12 cubic inches
Step 2: Convert the volume to cubic feet.
Since the weight of brass is given in lb per cubic foot, we need to convert the volume from cubic inches to cubic feet. There are 12^3 cubic inches in a cubic foot, so:
Volume in cubic feet = (π * [(17/32)^2 - (11/32)^2] * 12) / (12^3)
Step 3: Calculate the weight of material used in manufacturing one nozzle.
We know that brass weighs 520 lb per cubic foot, so:
Weight of one nozzle = Volume in cubic feet * Weight of brass per cubic foot
= (π * [(17/32)^2 - (11/32)^2] * 12) / (12^3) * 520 lb
Step 4: Calculate the total weight of material used in manufacturing 1000 nozzles.
To find the total weight of material used in manufacturing 1000 nozzles, we simply multiply the weight of one nozzle by 1000:
Total weight of 1000 nozzles = Weight of one nozzle * 1000
= [(π * [(17/32)^2 - (11/32)^2] * 12) / (12^3) * 520 lb] * 1000
Now, you can plug in the values and evaluate the expression to find the answer.