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Surface Area Show that the surface area of the cone
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Chapter 14 Solutions
Calculus: Early Transcendental Functions
- A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V=13R2H13rh2arrow_forwardSurface areas Use a surface integral to find the area of the following surfaces. The plane z = 6 - x - y above the square | x | ≤ 1, | y | ≤ 1arrow_forwardA). Use Pappus's theorem for surface area and the fact that the surface area of a sphere of radius d is 4pid^2 to find the centroid of the semicircle x=(d^2-y^2)^0.5arrow_forward
- Find the volumes of the solids The solid lies between planes perpendicular to the x-axis at x = 0 and x = 1. The cross-sections perpendicular to the x-axis between these planes are circular disks whose diameters run from the parabola y = x2 to the parabola y = sqrt(x).arrow_forwardFind the volumes of the solids The solid lies between planes perpendicular to the x-axis at x = 0 and x = 1. The cross-sections perpendicular to the x-axis between these planes are circular disks whose diameters run from the parabola y = x2 to the parabola y = √x.arrow_forwardArea of the plane region y=2x^2+1 and y=x^2+5arrow_forward
- Surface area using an explicit description Find the area ofthe following surfaces using an explicit description of the surface. The part of the plane z = x + 3y + 5 over the regionR = {(x, y): 1 ≤ x2 + y2 ≤ 4}arrow_forwardArea of Plane Region 3. R: x2 + 3y = 4 and x − 2y = 4arrow_forwardVolumes of solids Use a triple integral to find the volume of thefollowing solid. The solid in the first octant formed when the cylinderz = sin y, for 0 ≤ y ≤ π, is sliced by the planes y = x and x = 0arrow_forward
- Surface area using an explicit description Find the area ofthe following surfaces using an explicit description of the surface. The cone z2 = 4(x2 + y2), for 0 ≤ z ≤ 4arrow_forwardR zone; Being the first region of the coordinate plane bounded by the lines y=0, y=√3 and the circle x²+y²=9,Calculate the integral given in the picture.arrow_forwardVertical and Horizontal area of the plane region y=2x^2+1 and y=x^2+5arrow_forward
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