1. Your first task is to help Farmer Joe. He wants to fill his silo with soya beans and repaint the outside of it. He wants to know how much the silo will hold and how much paint he will need to paint it. The silo is 18' in diameter and 32.4' high, the height of the semi-circle top is 4'.a) Calculate the surface area of the box used, assuming there is no cardboard overlap.
break this into several problems. Total height of silo is 32.4ft heigth of cone is 4ft heght of cylinder will be 32.4-4 = 28.4 ft First you have a cylinder with a cone on top. these will be treated as 2 seperate object Surface Area = Areas of top and bottom +Area of the side Surface Area = 2(Area of top) + (perimeter of top)* height Surface Area = 2(pi r 2) + (2 pi r)* h We don't want the top and bottom of the cylinder so it is just pi*D*H 3.14 for pi. 28.4 = H 18 = D The amount of paint for the Cylinder part of the silo is 511.2 square feet The formula for the Volume of Cylinder is pi*r^2*H 3.14 for pi 28.4 = H 9=r The amount of grain is 7223.256 Cubic feet Formula for a cone's surface area is = pi*r^2 + pi*sqrt(r^2+h^2) we don't want the bottom of the cone so it is just pi*sqrt(r^2+h^2) Hight of cone = 4 radius of cone =( 3.14*sqrt(81+16) 3.14*sqrt (97) 3.14*9.848 Surface area of cone section = 30.923 square feet Volume of cone is (pi*r^2*h)/3 (3.14*81*4)/3 1017.36/3 = 339.12 Cubic feet Add the surface area together = 30.923 +511.2 = 542.123 square ft of paint Add the volumes together = 7223.256 + 339.12 = 7562.376 cubic feet of soybeans.
