Question 983851: I'm having a lot of trouble solving this word problem! Please help!
A silo is composed of a right circular cylinder with a right circular cone on the top of the cylinder that has the same radius. The height of the cone is half the height of the cylinder and the circumference of the cylinder is 20pi feet.
a.) Write the volume of the silo in terms of the height of the cylinder, h.
b.) If you want the volume of the silo to be 700 cubic feet, what should be the total height of the silo?
Answer by macston(5194)   (Show Source):
You can put this solution on YOUR website! .
a.) Write the volume of the silo in terms of the height of the cylinder, h.
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Circumference= pi x diameter
20pi ft=pi x diameter
20 feet=diameter
radius=(1/2)diameter=(1/2)20 feet=10 feet
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r=radius; h=height of cylinder
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Volume of cylinder=(pi)r^2h
Volume of cone=1/3(pi)r^2(1/2)h
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Volume of silo=volume of cylinder + volume of cone
Volume of silo=(pi)r^2h+(1/6)(pi)r^2h
Volume of silo=((pi)r^2h)(1+(1/6))
volume of silo=(7/6)(pi)r^2h=(7/6)(pi)(100h)=(116.67)(pi)h=(366.52)h
ANSWER: The volume of the silo is (366.52)h cubic feet.
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b.) If you want the volume of the silo to be 700 cubic feet, what should be the total height of the silo?
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700ft^3=(366.52)h
700/366.52=h
1.91 feet=h
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Height of silo=height of cylinder + height of cone
Height of silo=h+(1/2)h=(3/2)h=(3/2)(1.91 feet)=2.86 feet
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ANSWER 2: If the silo had a volume of 700 cubic feet and a diameter of 20 feet, its total height would be 2.86 feet.
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