My school is reviewing for CAPT, which is a state test given for sophomores. Please help me solve this problem:A farmer has two grain silos, both shaped like right circular cylinders, with dimensions shown in the diagrams below.Silo A has a height of 30 ft and a circumference of 12 ft. Silo B has a height of 30 ft and a circumference of 30 ftThe farmer has the same amount of grain stored in each of the two silos. Silo A is filled to the top. What is the height, in feet, of the level of the grain in solo B? Show your work or explain how you found your answer. Please show me how to do this problem thanks!
First, we need to find out the volume of grain in the filled silo. Volume for a right cylinder is the area of the circle times the height, V = π r^2 h. We don't know r, but we can figure it out from the circumference. Luckily, everything is in feet, so we don't have to worry about units. C = 2 π r 12 = 2 π r 12 / 2 π = r 6 / π = r (let's keep the π; hopefully, it will cancel out later; or we'll deal with it at the end) Now we can find the volume of the first silo. V = π r^2 h V = π (6 / π)^2 30 V = π (36 / π^2) 30 V = 1080 / π Now, we're told to find out how high the grain would be in the bigger silo. Again we need to find out what the radius of that silo is. C = 2 π r 30 = 2 π r 30 / 2 π = r 15 / π = r Let's plug that into our Volume formula for the large silo and solve for the height. V = π r^2 h 1080 / π = π (15 / π)^2 h 1080 / π = π (225 / π^2) h 1080 / π = (225 / π) h 1080 / π * (π / 225) = h 4.8 = h To answer the question: The grain in silo B would be 4.8 feet high.
