Use polar coordinates to find the volume of the given solid. bounded by the paraboloid z = 9 + 2x2 + 2y2 and the plane z = 15 in
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Answer:
88
Step-by-step explanation:
We can divide this into 3 shapes, a square, rectangle, and triangle.
Let's solve the area of each of these shapes and add them all up.
First, let's solve the square.
We know that one side is 4 ft so that means that the other side is also 4ft.
4*4=16
Our area of the square is 16ft^2
Let's solve the rectangle next,
Its length is 12ft and its width is 4ft.
12*4=48
So the rectangle area is 48ft^2
Now for the triangle
Remember that area of a triangle is a=hb/2
Our height is 12 ft and our base is 4ft
12*4=48
48/2=24
Triangle is 24ft^2
That means that we can add them all up
24+48+16=88
88ft^2 or 88
