Question 324934: A rancher outside houston decides to build a silo inside his corral. The rectangular corral measures 23 m by 17 m and the silo"s base is circular with a diameter of x meters. Find a polynomial for the remaining area of the corral
(in square meters) after the silo is built.
Answer by jessica43(140)   (Show Source):
You can put this solution on YOUR website! We are looking for the remaining area of the corral after the silo is built. In other words, find the total area of the rectangle and subtract the area of the silo base to get the remaining area:
R - S = A (R = rectangle area, S = silo base area, A = remaining area)
From there, we know we need to find the areas of both the rectangle corral and the silo so we can plug them into this equation.
Rectangle area:
We know that the corral measures 23m by 17m, and the area of a rectangle is length*width. So:
R=L*W
R=17*23
R=391
So the area of the rectangle corral is 391 square meters.
Silo base:
We know that the base is a circle with a diameter of x, and the area formula is S = πr^2 (where r=radius)
Since the radius equals half of the diameter (r=(1/2)x), our formula is:
S = π((1/2)x)^2
Now we can plug both of these equations into the first to creaet a polynomial for the remaining area of the corral in square meters:
R - S = A
391 - π((1/2)x)^2 = A
So this is your answer:
A = 391 - π((1/2)x)^2
|
|
|
