A grain silo is formed by attaching a hemisphere to the top of a right circular cylinder. If the cylinder is 18 ft tall and the volume of the silo is 486(pi) cubic feet, find the common radius of the cykinder and hemisphere
Volume of a cylinder = πr? h Volume of a hemisphere = (2π/3) r? You're given that h = 18 (ft) and that the total volume is 486π (ft?) 18π r? + (2π/3) r? = 486 π Multiply both sides by 3/(2π): 27r? + r? = 729 r? + 27r? - 729 = 0 Alas, this doesn't factor nicely. According to WolframAlpha, the equation has 3 real solutions, but two of them are negative and hence nonphysical. The one positive real root is approximately 4.7888.
