SOLUTION: 1) A circular flower garden has a diameter of 10 feet. One cubic yard of concrete is to be used to create a circular border of uniform width around the garden. The border is to

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Question 581366: 1) A circular flower garden has a diameter of 10 feet. One cubic yard of concrete is to be used to create a circular border of uniform width around the garden. The border is to have a depth of 3 inches. How wid will the border be?
2) An open box is to be made from a rectangular piece of tin whose length is twice its width. The box will be made by cutting a square of side 1 foot from each corner and folding up the edges. If the box needs to hold 4 cubic feet, what are the dimensions of the piece of tin?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Radius of garden = 5ft
Area of garden = pi*r^2
Area = 25pi
Let the uniform width be x
radius = (5+x)
Area of this circle = pi*(5+x)^2
Area = %285%2Bx%29%5E2%2Api
Area of the concrete portion = %28x%2B5%29%5E2%2Api-x%5E2%2Api
Area = %28x%5E2%2B10x%2B25%29%2Api-x%5E2%2Api
simplify
Area = (10x+25)*pi
Volume of the concrete portion = (10x+25)*pi*1/4 cu. ft
Quantity of concrete required = 1 cu.yard = 27cu.ft
(10x+25)*pi *1/3 = 27
10x+25 = (3*27)/(3.14)
10x+25 = 25.8
10x= 25.8-25
10x= 0.8
x= 0.8/10
x= 0.08 feet
x=0.96 in the width
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let the width be x
length = 2x feet

1 foot square cut off from corners
reduced length & width will be
x-2 width
length = 2x-2
height will be 1 foot
Volume = L*W*H
(x-2)(2x-2)*1
2(x-2)^2=4
(x-2)^2=2
take the square root
(x-2)= +/-sqrt(2)
x= 2+sqrt(2) Or 2-sqrt(2)
The width = 2+2sqrt(2)= 2(1+sqrt(2))
Length = 4(1+sqrt(2))