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| Math Central | Quandaries & Queries |
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Question from Taylor, a student: being 450pi (the area of a semi circle) how much money would it cost to lay carpet at $2.57 per foot??? if the area of a semi circular room is 450 pi ft then what is the volume being that the diameter is 60 feet and the ceiling is 16 feet tall |
Hi Taylor,
The semi circular room has a diameter of 60 feet so its radius is 60/2 = 30 feet. The area of a circle of radius 30 feet is π × 302 = 900 π square feet. The room is only half this size so its area is 450 π square feet. Since π is approximately 3.1416 this is 450 × 3.1416 = 1413.7 square feet. The cost to lay the carpet is $2.57 for every square foot so what will the cost be?
The room is the shape of a right, semi circular cylinder. Right means the walls are at a right angle to the floor and semi circular means the base is a semi circle. The volume is the area of the base times the height. Since your measurements are in feet the volume will be in cubic feet.
Penny
Taylor,
(1) theoretically, total cost is area x cost per unit area
(2) in practice you cannot buy curvilinear pieces of carpet; you will have to buy it in rectangular strips and throw some curved scraps away.
-RD
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