A silo is in the shape of a right circular cylinder with a hemispherical cap. Determine the radius r of the silo if the height of the silo is 25 ft and the volume is 935 ft^3. Write a function for the volume of the silo in terms of the radius. V=???I found that the radius is 3.45....but I'm not sure how to write the function. Help please!
The volume of the silo is: V=volume of cylinder + half volume of the sphere= Pi*r^2*h + (2/3)Pi*r^3 If you replace h by 25 and V by 935 you get an equation in r but it's not easy to solve it!
Well the volume is the volume of the regular cylinder plus the volume of the cap. The volume of the cylinder is h(pi)r^2. You found the radius to be 3.45. The trick is deciding what value to plug in for the height as the wording of the problem is a little ambiguous. If the value of 25 ft. they give includes the hemispherical cap then you will need to subtract from the 25 ft the radius. However, if by height they are strictly referring to the height of the cylinder without the cap then you leave h as 25. My guess is that they are including the cap so the volume of the cylinder is V = 21.55 (pi)r^2 Now find the volume of the cap which is (1/2)(4/3)(pi)r^3. So the total volume is V = 21.55(pi)r^2 + (2/3)(pi)r^3 :)
Well the volume of the silo is the volume of the cylinder and cap added together. So if we write these as the separate equations we get V = 2 Pi r^2 h and V = 2/3 Pi r^3 Then the volume of the silo is simply these added together. V = 2 Pi r^2 h + 2/3 Pi r^3. Now we know that h = 15, and we simply write V as V(r) to show its a function of r. This all gives V(r) = 50 Pi r^2 + 2/3 Pi r^3. If you wish you can simplify this to V(r) = Pi r^2(50 + 2/3 r) but there isnt really any need. Hope this helps. GL
This is a more tedious question than it first appears to be. The volume of the silo is the volume of the cap plus the volume of the cylinder. V = 4/6πr? + (25 - r)(πr?) (I assumed that the height of the cylinder was r less than the entire silo height of 25). No matter how you slice it, this is a cubic equation that in simplest form is r? - 75r? + (3)(935)/π = 0 This can be solved by graphing or by methods more fully explained in the source below. The radius you found is close, but it's not right. Try substituting it back into the original equation and see what you get.
