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math problem help! circular grain storage problem?
- h(t) = 100 - t^2/4 h'(t) = -2t/4 = -t/2 h'(10) = -10/2 = -5 5 m^3 of grain were removed on day 10.s
a silo is to hold 1000 m^3 of corn. what dimensions will minimize the surface area?
- You didn't say what shape the silo is to be. For a given volume, the minimum possible surface area is always a sphere. However, silos are usually cylindrical, so that's what I'll assume here. The volume of the silo = pi r^2 h where r is its radius and h is its height. So, pi r^2 h = 1000 Its surface area A = pi r^2 + 2 pi r h h = 1000 / (pi r^2) So A = pi r^2 + 2 pi r [1000 / (pi r^2)] = pi r^2 + 2000/r The minimum surface area is found by setting dA/dr = 0 dA/dr = 2 pi r - 2000/(r^2) So 2 pi r - 2000/(r^2) = 0 2 pi r = 2000/(r^2) r^3 = 1000/pi r = (1000/pi)^(1/3) h = 1000/(pi r^2) = (1000/pi)(r^3)^(-2/3) = (1000/pi)(1000/pi)^(-2/3) = (1000/pi)^(1/3) = r So, the surface area of the silo is minimised if r = h = (1000/pi)^(1/3) = 6.83 metres (approx.)s
If you lived in a circular brick house with no windows could?
- Very little.s
How do I solve this problem?
- The volume of any prism is the area of the face multiplied by the height. The height is given, so all you need to find is the area of the base. Start off by drawing a circle. One side has a chord of length 10 feet cut across it. Its given that the chord is 5 feet from the center of the circle. Therefore, you draw a line from the center bisecting the chord, as well as a line from the center to each end of the chord (the radius), and you have two equal isosceles triangles with two sides of length 5. Pythagorean's relation tells us that the third side has a length of 5*sqroot(2) ft. Now that you have the radius, you can find the area of the circle. However, its not a true circle you're concerned with. You want to exclude the area on the outside of the chord. Using trig, you can find that the total angle subtended by the chord is 90°. Therefore, the area that you're concerned with is the circular area for the outside 270° plus the area of the triangles. 270° is (3/4) of the circle, so its area is (3/4) the area of the entire circle. A = (3/4)*π*r² = (3/4)*π*(5*sqroot(2)ft)² = 118ft². The area of each of the smaller triangles is given by (1/2)*b*h. Since there's two triangles, the total area of the two is 2*(1/2)*b*h = b*h = 5ft*5ft = 25ft². The total area of the base is 118ft² + 25ft² = 143ft². Multiplied by the height will give the total volume of the prism, 143ft²*30ft = 4290ft³.s
what is the formula for figuring grain storage capacity?
- hey ....Cubs; Volume of a cylinder is: Area=Pi times the square of the radius. This times the height of the cylinder will yield the volume. If the container is square multiply three sides to get the volume.s
What is the surface area of a silo? Geometry?
- r=9' surface area of the dome is 4pr2/2=509 sq ft that means the silo's walls are 41' tall, with a circumference of 56.54', which means the surface area of the wall is 2,318 sq ft... 2,318 + 509= 2,827 sq ft of surface area 2,827 / 250= 11.308 gallons x $1k/gallon=$11,308.s
Can the physics of putting your finger over a straw engulfed in water be enlarged to a bigger scale, say the size of a silo?
- It might be able to be scaled up, but there is a point that gravity and the strength of the materials would cause it to fail.s
How come the Amish folk never get together on weekends and throw up a skyscraper?
- Hmmm....maybe they'll only go up to the height of a silo. :)s
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