Quiz on Surface Area10 points for best quickest repliesA farmer in Iowa must periodically resurface the interior (wall, floor and ceiling) of his $350,000 silo. The compound to resurface the silo protects the interior from the acid created by the silage. The height of the silo to the top of the hemispherical dome is 50 feet and the width is 18 feet. With this information please answer the following questions.1. What is the interior surface area of this silo?2. If one gallon of resurfacing compound covers 250 square feet, how many gallons are needed to resurface the entire interior of the silo?3. Each gallon of resurfacing compound costs $1000. What is the total cost to resurface the silo.4. Each bushel of silage has a density of 0.8 cubic feet. Approximately how many bushels of silage are required to completely fill your silo?5. What percentage (%) of the farmer's initial silo expenditure is this resurfacing project?
r=9' surface area of the dome is 4pr2/2=509 sq ft that means the silo's walls are 41' tall, with a circumference of 56.54', which means the surface area of the wall is 2,318 sq ft... 2,318 + 509= 2,827 sq ft of surface area 2,827 / 250= 11.308 gallons x $1k/gallon=$11,308.
1 - get the height of the cylindrical portion, or total height - height (radius) of hemisphere r = 18 / 2 = 9 ft h(cyl) = 50 - r = 41 ft now, for the surface area, we have three pieces hemisphere SA = 4*pi*r^2 / 2 = 2 * 9^2 * pi = 162pi floor (circle) = pi*r^2 = 81pi wall(cylinder - caps) = 2*pi*r*h = 2*9*41*pi = 738pi add them: (81+162+738)pi = 981pi = 3082 square feet 2 - Simple division: 981pi sqr ft / 250 gal / sqr ft = 3.924pi = 12.33 gallons 3 - Simple multiplication 3.924pi gallons * 1000 dollars/gallon = $3924pi = $12328 4 - .8 cubic feet is not a density, it's a volume, but we'll move on. Need to find the volume of the silo. For the cylinder: V (cyl) = pi*r^2*h = 9^2 * 41 * pi = 3321pi for the hemisphere: V (hemi) = (4/3)*pi*r^3 / 2 = (2/3)*9^3*pi = 486pi add them; (3321 + 486)pi = 3807pi = 11 960 cubic ft Now, divide by the volume of a bushel to determine how many bushel this represents 3807 cubic ft / .8 cubic feet / bushel = 4758.75pi = 14950 bushels 5 - ($3924pi / $350000 ) * 100% = 3.522%
