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.
Okay, you've got to combine a couple of equations here: Surface area of a cylinder = 2πr^2 + 2πrh So, because you won't be painting a flat top or a bottom, we'll ditch that part of the equation, leaving us with 2πrh. Now, since we've got a half-sphere as our top, we need to use the surface area of a sphere equation, which is 4πr^2. BUT, since we only have half of a sphere, lets divide that by 2. (4πr^2)/2 So now, to find the surface area of the WHOLE thing, combine our two equations. Silo + Top 2πrh + (4πr^2)/2 Now insert your values, plug and chug. 2π9(<---Because the radius is half of the diameter)32.4 + (4π(4^2))/2 583.2π + (4π16)/2 583.2π + 32π is the surface area. To find volume, we use even MORE equations. We'll need the volume of the cylinder, which is π(r^2)h And the volume of a sphere, which is (4/3)π(r^3) But remember, since we only have half of sphere on top, we'll need to divide that equation by two. ((4/3)π(r^3))/2 Once again, we'll combine the equations. Silo + Top π(r^2)h + ((4/3)π(r^3))/2 And then plug and chug. π(9^2)32.4 + ((4/3)π(4^3))/2 π(27)(32.4) + ((4/3)π(64))/2 π874.8 + 42.67π is the volume. Remember to add your units! They should be feet squared for surface area and feet cubed for volume.
