A silo, used to store grain and corn, is in the shape of a cylinder with a hemisphere on top. Height of silo is 100ft.a. What is the volume (capacity) of a silo that is 20 feet in diameter?b. What is the surface area of the silo?
V(silo) = V(cylinder) + V(hemisphere) or V(silo) = V(cylinder) + 1/2*V(sphere) V(cylinder) = area of base(circle) * height radius= 1/2 diameter = 20/2 = 10 ft V(cylinder) = 2*pi*r? * h = 2*pi*100 = 200*pi V(sphere) = (1/2)4/3*pi*r? = 4/3*1000*pi = 2000/3*pi V(silo) = (200+2000/3)pi = 2600/3pi = 766.6667 cu ft SA(silo) = SA(cylinder) + 1/2*SA(sphere) SA(cylinder) = 2*pi*r*h = 2*10*100*pi =2000pi SA(sphere) = 4*pi*r? 1/2*SA(sphere) = 1/2*4*pi*r? = 2*100*pi = 200pi SA(silo) = (200+2000)pi = 2200pi = 6911.503 sq ft
I noticed an error or two in the previous answer, so here's my shot at it. My answer is based on the 100 ft including the height of the hemispherical portion; if you meant to say that 100 ft is the height of just the cylinder portion, please accept my apologies..... D = 20 ft r = D/2 = 10 ft height of cylinder = (hc) = 100 - r = 90 ft a. V = Cylinder volume + Hemispherical volume V = pi*r^2*(hc) + (2/3)*pi*r^3 V = 9000*pi + (2000/3)*pi V = (29000/3) * pi V ~ 30,368.73 ft^3 b. SA = SA of cylinder + SA of hemisphere SA = 2*pi*r*(hc) + 2*pi*r^2 SA = 1800*pi + 200*pi = 2000*pi SA ~ 6283.18 ft^2
