EXAMPLE 1 Estimate the volume of the solid that lies above the square R [o, 10]
ID: 3283458 • Letter: E
Question
EXAMPLE 1 Estimate the volume of the solid that lies above the square R [o, 10] x [o, 10] and below the elliptical paraboloid z 404 -x* - 3y. Divide R into 4 equal squares and choose the sample point to be the upper right corner of each square Riy. Sketch the solid and the approximating rectangular boxes SOLUTION The paraboloid is the graph of f(x, y) - 404 - x2- 3y and the area of each square is Approximating the volume of the Riemann sum with m = n = 2, we have S, 5)AA, 10)AA+ (10, S)AA 10, 10JAA = Video Example) Tutorial 304 79 25)( (25) 4(25)- Online Textbook This is the volume of the approximating rectangular boxes shown in the figure.Explanation / Answer
The paraboloid is the graph of f(x,y)=404-x^2-3y^2 and the area of each square is 25 . Approximating the volume of the riemann sum with m=n=2, we have
V= ......
=.......
=304 (25) + 79 (25) + (404-100-75) (25) + 4 (25)
=7600 + 1975 + 5725 + 100
= 15400
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