SOLUTION: 1)You are designing a rain gutter made from a piece of sheet metal 1 foot by 5 feet. The gutter will be formed by turning up two sides. You want the gutter to have the greatest v
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Question 425090: 1)You are designing a rain gutter made from a piece of sheet metal 1 foot by 5 feet. The gutter will be formed by turning up two sides. You want the gutter to have the greatest volume possible.
a.How much should you turn up?
You can put this solution on YOUR website! You are designing a rain gutter made from a piece of sheet metal 1 foot by 5 feet.
The gutter will be formed by turning up two sides.
You want the gutter to have the greatest volume possible.
;
a.How much should you turn up?
Change the width of the sheet metal to 12 inches
:
The end of the gutter sort of looks like this x|__|x
x = the height of the gutter, (the amt turned up)
then
12 - 2x = the width of the gutter
:
Greatest volume with be determined by the greatest cross section area
A = x(12-2x)
A = -2x^2 + 12x
Find the axis of symmetry to find the height with the greatest area
x = -b/(2a); in this equation a=-2, b=12
x = -12/(2*-2)
x = 3 inches is the height for the greatest cross sectional area
then
12 - 2(3) = 6 inches is the width of the gutter
3 * 6 = 18 sq inches is the cross sectional area
:
b. What is the maximum volume?
18 *5(12) = 1080 cu/inches
or = .625 cu ft
