Mathematics | Area of the surface of solid of revolution Improve Improve Like Article Like Save Share Report Consider a plane y=f(x) in the x-y plane between ordinates x=a and x=b. If a certain portion of this curve is revolved about an axis, a solid of revolution is generated. We can calculate the area of this revolution in various ways such as: Cartesian Form: Area of solid formed by revolving the arc of curve about x-axis is- Area of revolution by revolving the curve about y axis is- Parametric Form: About x-axis: About y-axis: Polar Form: r=f(θ) About the x-axis: initial line Here replace r by f(θ) About the y-axis: Here replace r by f(θ) About any axis or line L: where PM is the perpendicular distance of a point P of the curve to the given axis. Limits for x: x = a to x = b Here PM is in terms of x. Limits for y: y = c to y = d Here PM is in terms of y. Example: Find the area of the solid of revolution generated by revolving the parabola about the x-axis. Explanation: Now we are given with the Cartesian form of the equation of parabola and the parabola has been rotated about the x-axis. Hence we use the formula for revolving Cartesian form about x-axis which is: Here . Now we need to calculate dy/dx Differentiating w.r.t x we get: Using Now we are provided with limits of x as x=0 to x=3. Plugging our calculated values in the above formula we get: Last Updated : 10 May, 2020 Like Article Save Article Previous Roots of Unity Next Maximum sum of values of nodes among all connected components of an undirected graph Share your thoughts in the comments Add Your Comment Please Login to comment...