1. Consider the region bounded by the graphs of x = y² and x = 9. Find the volume of the solid that has this region as its base if every cross section by a plane perpendicular to the x-axis has the shape of an equilateral triangle. (Hint: Precalc review...if one side of an equilateral triangle is s, then the area of the triangle is s2). y

Q: The volume of the region bounded by x + y +z = 1 is 2л а. 3 2л 4 472 с. 3 d. None of these b.

A: The given equation x2+y2+z2=1, is a equation of a sphere equation of a sphere centered at origin and…

Q: 4. Find the volume of the region bounded above by the paraboloid z = x? + y? and below by the…

A: (4) Consider the provided question, According to the provided question, draw the graph of the given…

Q: Let B be the solid whose base is the circle x^2+y^2=49 and whose vertical cross sections…

A: Given, Circle- x²+y²=49=7² --------equation 1 The equation is of the form x²+y²=r². Therefore, the…

Q: Evaluate , ydV where E is the hemispherical solid region x? + y? + z? 0.

A: x^2+y^2+z^2 <=64, y>=0

Q: b) Find the volume of the region in the first octant bounded by the planes shown in the figure.…

A: Given: The equation of the plane is  y + z = 2 The equation of the cylinder is  x = 4 − y2 he volume…

Q: Find the volume of the torus generated by revolving the region bounded by the graph of the circle…

A: given x-112+y2=1 claim- to find the volume of torus generated by revolving the region bounded by the…

Q: If the area bounded by y = x² and y = 2 – x² is revolved about the x – axis and a vertical…

A: We have to find the volume of the solid if the area bounded by y=x2 and y=2-x2 is revolved about the…

Q: Suppose that R is the finite region bounded by y = 1, y = x + 5, x = 0, and z = 4. Find the exact…

A:

Q: Let B be the solid whose base is the circle (x^2) + (y^2) = (4^2)  and whose vertical cross sections…

A: This question is based on application of Integration.

Q: Given an area D bounded by curve y = 4x−x^2, line x+y = 6, and y-axis. Find the volume if the area D…

A: We are given an area D bounded by curve y = 4x - x2, line x + y = 6, and y-axis. We need to find the…

Q: The region bounded by y = 0 and y = kx – x is revolved around the y-axis to form a solic whose…

A: Given,        y=0, and  y=kx-x2

Q: 1. Use the general slicing method to find the volume of the following solid. The solid whose base is…

A:

Q: the are bounded by the parabola ay=x², the x-axis, and the line x=b is revolved about the y-axis.…

A: Let us have two curves x=fy, x=gy Here, gy is to the right of fy When the value of y is from c to d…

Q: 27. Find the volume of an ice cream cone bounded by the hemisphere z '8 – x² – y² and the cone z Va2…

A: Given hemisphere z=8-x2-y2 and cone z=x2+y2 The intersection of hemisphere and cone is given by…

Q: Show that the volume generated by revolving the region in the first quadrant bounded by the…

A: Solution is below.

Q: 27. Find the volume generated by rotating the area bounded by y = x² + x, x = 1, x = 4, and the…

A: Given that: y=x2+x,   x=1,  x=4   and   the   x-axis To sketch the graph,

Q: A volume is described as follows: 1.  the base is the region bounded by x=−y^2+10y+93 and…

A: The base of the object is the region bounded by x=−y2+10y+93 and x=y2−30y+243 Every cross-section…

Q: 4. Find the volume of the region bounded by y = -x+1, x = 0 and y = 0 revolved about the x-axis.

A:

Q: Suppose that R is the finite region bounded by y = x, y = x + 3, 0, and x 1. Find the exact value of…

A:

Q: Suppose that RR is the finite region bounded by  y=x, y=x+4, x=0, and x=2. Find the exact value of…

A:

Q: Given the region bounded by y=×^3 ,X = 2, and the x-axis (in Quadrant I) is rotated about the line y…

A:

Q: The base of the solid S is the region enclosed by the graph of y=sqrtln(x), the line x=e and the…

A: Given The base of the solid S is the region enclosed by the graph of y=sqrtln(x), the line x=e and…

Q: b) Find the volume of the solid which is in the first octant and bounded between the spheres p = 1…

A: To find- Find the volume of the solid which is in the first octant and bounded between the spheres ρ…

Q: 5. Ay 1 y = ycos x π 4.

A: Apply the washer method; The volume of revolution of the curve about x-axis, from x = a to x = b is…

Q: Define Q as the region bounded by the functions f(x)=x^2/9 and x=2 in the first quadrant between y=2…

A: Use the washer's method to solve the problem. The volume of the solid is given by V=π∫cdfy2-gy2dy.

Q: 4. Find the volume of the region bounded by y = - x+1, x = 0 and y = 0 revolved about the x-axis.

A:

Q: 14. Find the volume tended by the graph of f(x, y) = 1+2x + 3y, the rectangle [1, 2] x [0, 1], and…

A: Given function is: fx,y=1+2x+3y and the coordinate of the rectangle is: 1,2×0,1

Q: For this problem, consider the region bounded by y=1+Vr, x=4, and y= 1. Set up, BUT DO NOT EVALUATE,…

A: The given region is bounded by the curves  y=1+x,  x=4,  y=1 The region is to be revolved around the…

Q: A volume is described as follows: 1. the base is the region bounded by - y' + 4y + 147 and 2 x = y –…

A:

Q: Suppose that a region R has area A and lies above the x-axis. When R is rotated about the x-axis, it…

A: Use the disc method to find the W in terms of V, k and A.

Q: Suppose that R is the finite region bounded by f(x)=√x and f(x)=x3. Find the exact value of the…

A:

Q: Q6 If the region bounded by 1 y X = 1 and x = 2 %3D is revolved about the y-axis , then the volume…

A:

Q: Suppose that R is the finite region bounded by y = x, y = x + 1, x = 0, and x = 2. Find the exact…

A:

Q: Find the volume of the region inside both z2 + 4 = x² + y² and x2 + y? + z2 = 16.

A: Given that, z2+4=x2+y2, x2+y2+z2=16 Intersection of both curve is, x2+y2+x2+y2-4=16x2+y2=10 So the…

Q: 9) Find the volume of the region bounded by y = x + 1 x +1' Y = 0, x = 0, and у %3D0, х%3D x = 4…

A: The formula for the washer method around the x-axis is V=π∫abf(x)2-g(x)2dx where f(x) is the top…

Q: Let M be the region in the first quadrant bounded above by the graph of y = 3x and below by the…

A:

Q: Find the volume.

A:

Q: If the region bounder by the two curves is revolved about x = 4, what is the volume of the resulting…

A:

Q: Given the region bounded by y= x^3 ,x = 2, and the x-axis (in Quadrant I) is rotated about the line…

A: Given problem:- Given the region bounded by y=x3 ,X = 2, and the x-axis (in Quadrant I) is rotated…

Q: 3. Find where the curves intersect, draw a sketch of the region, and compute the volume when the…

A:

Q: 3. Find the volume of the region common to the interiors of cylinders a? + y² = 1 and r? + z2 = 1

A:

Q: Find the volume of the banded region by the surfoce fixylƏxy on the region 1ラ×ラ

A:

Q: Graph the region bounded by the curves y=x+2, y=x+7, x=0, and x=6  uses the washers method to find…

A: The equation of the curves are: C1: y = x+2C2: y = x+7C3: x = 0C4: x = 6 Axis of rotation: x-axis To…

Q: A volume is described as follows: 1. the base is the region bounded by æ = - y? + 10y + 95 and æ =…

A:

Q: If the volume of the region bounded above by z = a²-x² - y2, below by the xy-plane, and lying…

A: Please see the attachment

Q: 5. Find the volume generated by the areas bounded by the straight line y = x, between y = 0 and x =…

A:

Q: 2. Find where the curves intersect, draw a sketch of the region (label it completely), and compute…

A: Region is sketched. And volume is evaluated.

Q: Given the area in the first quadrant bounded by x²=8y, the line y-2=0 and the y-axis, what is the…

A:

Q: Find the volume of the solid in the Ist quadrant under the graph of z= f(2, y) = 3- VP+y² and inside…

A:

Q: 4. Sketch the region, draw in a typical shell, identify the radius and height of the shell, and…

A: Please see the attached picture on the white board.The shaded region in the top figure is the…