Four Circular wheat silo's are arranged so that each circular silo touches two other silo's at exactly one point. (So basically the Silo's are arranged in 2 rows of 2)When the silo's are filled, the grain overflows to fill the space in between all four Silos.The radius of each Silo is 2 meters, the height is 10 meters.What would be the the total volume of the four Silos and the space in between them?Please show the steps taken to solve this problem. Much appreciated.Thanks.
Volume of one silo = (pi)(r^2)(h) = 3.14(4)(10) = 125.6m^3 Volume of four silos = 4(125.6) = 502.4m^3 Space between the silos is roughly a square with a side of 2 (not exact but damned close): V = 2^2(10) = 40m^3 Total volume = 502.4 + 40 = 542.4m^3 -.--
Looking down from above, the area encompassed by drawing lines from the center of each silo to the centers of the 2 silos it touches is a square with side = 2x2 = 4 meters. This square takes up the center area, plus 1/4 of the area of each silo. volume of square cylinder (square x 10 meters high) = 160 m^3 Remaining volume of 4 cylinders = 4 (3/4) π (2^2) 10 = 376.8 m^3 Total volume = 536.8 m^3
Volume of each silo = Pi*r^2*h, where r-radius h-height = Pi * 4 * 10 = 40Pi m^3 Therefore, total volume of 4 silos = 4 *40Pi = 160 Pi m^3 With the above arrangement of silos it is obvious that the lines joining the centers of the 4 silos form a square of 4m side each. Therefore, the total volume of the space between the silos can be evaluated by subtracting the the volume of 4 quarter silos from the the volume of the square prism ( of side -4m height - 10 m). Volume of the square prism = Area * height = (4*4) * 10 = 160 m^3. Total volume contributed by the 4 quarter silos = Volume of a single silo = 40 Pi m^3. Hence, the total volume of the space between the silos = 160 - 40 Pi = 160 - 125.66 = 34.34 m^3(appx)
