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(22740)   (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
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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)
:
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