The volume of the hopper bin is the amount of feed in it
- The volume of the hopper bin is 35974 cubic feet
- The carnival tent can be filled to 85% of its volume and not exceed the weight limit
<h3>The volume of the hopper bin</h3>
The given parameters are:
- Height of cylinder, H = 20 ft
- Diameter of cylinder, D = 36 feet
- Angle, θ = 52°
Start by calculating the radius (r) of the cones.
r = D/2 -------- because the cones and the cylinder have equal diameters.
So, we have:
r = 36/2 = 18
The height (h) of the cones is:
tan(θ) = h/r
This gives
tan(52) = h/18
Make h the subject
h = 18 * tan(52)
Evaluate
h = 23.04
The volume is then calculated as:
Volume = Volume of cylinder + 2 * Volume of cone
This gives
Volume = πr^2H + 2 * 1/3πr^2h
Volume = πr^2H + 2/3πr^2h
Factor out πr^2
Volume = πr^2(H + 2/3h)
Substitute known values
Volume = 3.14 * 18^2 * (20 + 2/3 * 23.04)
Evaluate
Volume = 35973.85 cubic feet
Hence, the volume of the hopper bin is 35974 cubic feet
<h3>The weight limit of the hopper bin</h3>
The given parameters are:
- Maximum weight = 500000 pounds
- Feed weight = 22 pounds per cubic feet
For a feed that weighs 22 pounds per cubic feet, the weight of the hopper bin would be:
Weight = 22 * 35974 pounds
Weight = 791428 pounds
At 85% full, the weight wuld be:
Weight = 85% * 791428 pounds
Weight = 672713.8 pounds
672713.8 pounds is greater than the weight limit of 500000 pounds.
Hence, the carnival tent can be filled to 85% of its volume and not exceed the weight limit
Read more about volumes at:
brainly.com/question/3989169
