# SOLUTION: Hi, can you help me with this problem? A storage bin for corn consists of a cylindrical section made of wire mesh, surmounted by a conical tin roof, as shown in the figure. The

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 Question 119838: Hi, can you help me with this problem? A storage bin for corn consists of a cylindrical section made of wire mesh, surmounted by a conical tin roof, as shown in the figure. The height of the roof is one-third the height of the entire structure. If the total volume of the structure is 2900 ft3 and its radius is 9 ft, what is its height? (Round the answer to one decimal place.) Answer by ankor@dixie-net.com(15652)   (Show Source): You can put this solution on YOUR website!A storage bin for corn consists of a cylindrical section made of wire mesh, surmounted by a conical tin roof, as shown in the figure. The height of the roof is one-third the height of the entire structure. If the total volume of the structure is 2900 ft3 and its radius is 9 ft, what is its height? (Round the answer to one decimal place.) : Let h = height of the cylindrical section only Then .5h = height of the conical section only (.5h is 1/3 of 1.5h, the total height) : We know: vol of a cylinder = pi*r^2*h vol of a cone = (1/3)*pi*r^2*h : Given: Vol of the cylinder + vol of the cone = 2900 cu/ft : pi*9^2*h + (1/3*pi*9^2*.5h = 2900 : pi*81*h + (1/3)*pi*81*.5h = 2900 : pi*81*h + pi*27*.5h = 2900; took (1/3) of 81 : 254.469h + 42.4115h = 2900 : 296.88h = 2900 : h = 2900/296.88 : h = 9.768 ft is the height of the cylinder : 4.88 ft is the height of the cone : 9.768 + 4.88 = 14.6 ft is the total height : : Check solution using 9.8 for ht of the cylinder and 4.9 for the ht of the cone pi*9^2*9.8 = 2493.8 cu ft (cylinder) (1/3)*pi*9^2*4.9 = 415.6 cu ft (cone) 2493.8 + 415.6 = 2909.4 ~ 2900 (we rounded both values upward) : Did this help?