A grain silo consists of a cylindrical main section and a hemispherical roof. If the total volume of the silo (including the part inside the roof section) is 10,000 ft3 and the cylindrical part is 30 ft tall, what is the radius of the silo, correct to the nearest tenth of a foot?r=__ftplease someone help me i keep getting the answer wrong! erg!
the quantity of the silo is: pi*r^two*h+(four/3pi*r^three)*one million/two the primary quantity is is the quantity of the cylindrical major segment and the following one is the quantity of the hemispherical roof. 15000=pi*r^two*(30)+(two/three)pi*r^thre... component out a pi*r^two 15000=pi*r^two(30+(two/three)r) now remedy for r 15000=pi*r^two or 15000=30+(two/three)r r=eight.31ft or r=22455
your best bet here is to first try and write out an equation that you can solve.... i like to always start with the very basic concepts, so that you know where to go and what to do... naturally, when applying this method to other problems, knowing formulas will come in handy.... here is what you have at the very core: Total Volume = Volume of a Cylinder + Volume of 1/2 Sphere (same as hemisphere) from here, plug in ALL of the numbers you know and lets start solving Total Volume = 10,000 Volume of Cylinder is: pi * r^2 * height, so this part is pi * r * 30 Volume of a Sphere is: 4/3 * pi * r^3, so this part is 4/3 * pi * r^3 lump all that junk together.... 10,000 = (30pi * r^2) + 1/2 *(4/3 * pi * r^3) at this point, you have a few options...i am gonna multiply everything by 6 to get rid of the fractions from the sphere portion..giving us: 60,000 = 180pi * r^2 + 4pi * r^3 again, you have an option here (approximate pi now, or later). keep in mind rounding off pi now can cause the answer to be less accurate. what you do now is put everything on one side, so we can graph this on a graphing calculator....since solving this by factoring is all but impossible due to the pi's. so, graph: y = 4pi r^3 + 180pi r^2 - 60000 on your calculator. (use x instead of r, use the pi symbol on your calculator) for best results, set your window to the following settings: xmin: -50 xmax: 25 xscale: 10 ymin: -200,000 ymax: 200,000 yscale: 50,000 now, last but not least, we can look for the zero's...since we are really talking about r and not x, we know that they cant be either of the two negative zero's, because we cant have a negative radius....that being said, use your calculators menu to find the value of the single positive zero. you should find it to be: 9.3710218 round it off accordingly. you can also go back and plug that value in to test it. though you will not get 10,000 exactly, it will still be very close. hope this helped! good luck
