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?
2007-10-01 04:36:52 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
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*r² * h = 2*pi*100 = 200*pi
V(sphere) = (1/2)4/3*pi*r³ = 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*r²
1/2*SA(sphere) = 1/2*4*pi*r² = 2*100*pi = 200pi
SA(silo) = (200+2000)pi = 2200pi = 6911.503 sq ft
2007-10-01 05:15:43 · answer #1 · answered by 037 G 6 · 0⤊ 0⤋
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
2007-10-01 12:50:30 · answer #2 · answered by The K-Factor 3 · 1⤊ 0⤋