Cylinder volume? A lie-down cylinder?

Question

I have a cylinder of 5-m diameter and 12-m length. The cylinder is not vertical, but horizontally placed so that the height of the cylinder becomes the length. Sand of height 1-m, measured vertically from the bottom of the horizontal cylinder, accumulate along the cylinder length. How much in terms of volume does the sand occupy in the horizontal cylinder? I need the formula. Thanks.

Answer 1

IN CASE OF LIE DOWN CYLINDER, THE CROSS SECTION FORMS A SEGMENT OF A CIRCLE
then
volume of a segment of circle = 3.14* height^2 *(3*radius- height)/3
=3.14* 1^2 *(3*5 - 1)/3
=14.65 m^3
therefore sand volume is 14.65 m^3

Answer 2

I only have the basic formulas. But I think you are able to use the basics to find the answer.
Picture we are looking at the cross section. We see 1 circle with 1m of sand. At the edge of the sand and circle to the centre of the circle, the length is the radius = 2.5m
From the top of the sand, the length to the centre of the circle is radius - 1m = 2.5 - 1 = 1.5m
Now, we find the angle from 1 edge of the sand to the other. But before that, we find half of it 1st as such
2.5cosA = 1.5
The angle between the 2 edges is 2A.
Now, you use pi x r^2 x 2A/360, you'll find the area of the segment of the circle.
Next thing you have to deduct the area of the triangle from the segment and you'll get area of the sand. Multiply by the length and you'll get the answer you want

Answer 3

In order to answer this question, you will need to find the area of the cross-section of fuel in terms of the height, h. Draw a circle. Next, draw a chord of the circle below the center, as if the tank is less than half-full. The perpendicular distance from this line to the bottom of the tank is h. Next draw a line from the center of the circle to the "corner" where the fuel line meets the circle. This is a radius of 18 inches. Also draw in the other radius to the other "corner". Drop a perpendicular from the center of the circle to the fuel line. This distance is 18 - h. You now have two right triangles with hypotenuse 18 and height 18 - h. Next, you will need to find the area of these triangles, then subtract that answer from area of the sector of the circle. That will give you the cross section. From there you should be able to find the volume of fuel left by multiplying the cross-section area of the fuel by the length of the tank, which I believe is about 68 inches. The work for that is below. Good luck. To find the length of the tank, we need to know what 300 gallons is in cubic inches. It's 69,300. Next, find the length: 69300 = pi*18^2*L ---> L = 69300/(pi*18^2) = 68 inches

Answer 4

The volume of the sand is the area of the sector filled with sand times the length. The area of the sector is the area of the segment minus the area of the triangle
V = L[(1/2)R^2(2arccos((R - h)/R) - (1/2)(R-h)(2√(R^2 -(R - h)^2))]
w = 2√(R^2 -(R - h)^2)
w = 2√(5^2 - 4^2) = 6
θ = 2arccos(0.8) = 1.287
V = 12(0.5*25*1.287 - 0.5*4*6)
V = 12*4.0875
V = 49.05 m^3

Answer 5

Pi 3.14 X Radius squared X Height. What's the difference if it is vertical or horizontal. The volume is a constant.