A silo consists of a cylindrical body and a hemispherical roof is used to store the harvested grain. The height of the cylinder is 9m. The total volume of the silo including the part inside the roof section is 425m^3 . What is the radius of the silo?(i) What do you know about this problem? That is write down all the data obtained from given question. Hence write all the equation of volume of the silo with radius r as the only unknown variable.(ii) What do you not know about this problem?Explain why you cannot solve this problem(iii) You can get an appoximate answer to the above problem. Explain or show how you can accomplish this task
Volume of cylinder=22/7*r^2*h eq(1) where 22/7=pie. r=radius of cylinder h=height of cylinder Volume of hemisphere= 2/3*22/7*r^3 -----------------eq(2) where 22/7=pie r=radius of hemisphere According to given data Total volume of silo is 425 m^3 -------------eq(3) Therefore from eq 1,2 and 3 22/7*r^2*h +2/3*22/7*r^3 =425 I think that hint works for you
Volume of cylinder = (pi)(radius)^2 (height) Volume of hemisphere = (1/2)(4/3)(pi)(radius)^3 = (2/3)(pi)(radius)^3 Volume of silo = volume of cylinder + volume of hemisphere = (pi)(radius)^2 (height) + (2/3)(pi)(radius)^3 = (pi)(r^2)(9) + (2/3)(pi)(r^3) Note that the radius of the base of the cylinder must be the same as the radius of the hemisphere. So... Volume = (pi)(r^2)(9) + (2/3)(pi)(r^3) You would need to solve this equation: 425 = (pi)(r^2)(9) + (2/3)(pi)(r^3)
