SOLUTION: An aluminum plate is made according to the following dimensions. The outer radius is 10 inches and the inner radius is 3 inches. Use p = 3.14 as an approximate value. (a) How many

Question 150476: An aluminum plate is made according to the following dimensions. The outer radius is 10 inches and the inner radius is 3 inches. Use p = 3.14 as an approximate value. (a) How many square inches in area is the aluminum plate (b) If the cost to construct the plate is $7.50 per square inch, what is the construction cost?

Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
An aluminum plate is made according to the following dimensions. The outer radius is 10 inches and the inner radius is 3 inches. Use p = 3.14 as an approximate value. (a) How many square inches in area is the aluminum plate (b) If the cost to construct the plate is $7.50 per square inch, what is the construction cost?
.
The aluminum plate is "round" (10 in radius) with a hole in the middle (hole has a 3 inch radius).
.
Part a:
"area of plate" = "area of circle w/10 in. radius" - "area of hole in middle"
.
"area of a circle" = (1/2)(pi)(r^2)
.
"area of plate" = [(1/2)(3.14)(10^2)] - [(1/2)(3.14)(3^2)]
"area of plate" = [(1/2)(3.14)(100)] - [(1/2)(3.14)(9)]
"area of plate" = (1/2)(3.14)[100-9]
"area of plate" = (1/2)(3.14)[91]
"area of plate" = 142.87 sq inches
.
Part b:
"cost" = 7.50(142.87) = $1071.53

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