How to find the volume of the solid generated by revolving?

Example 1: Find the volume of the solid generated by revolving the region bounded by y = x 2 and the x ‐axis on [−2,3] about the x ‐axis. Because the x ‐axis is a boundary of the region, you can use the disk method (see Figure 1 ). Figure 1 Diagram for Example 1.

How do you find the radius and height of a revolution?

If, however, the axis of revolution is horizontal, then the radius and height should be expressed in terms of y. The volume ( V) of a solid generated by revolving the region bounded by y = f (x) and the x ‐axis on the interval [ a,b ], where f (x) ≥ 0, about the y ‐axis is

How do you find the radius of a perpendicular disk?

If a disk is perpendicular to the y ‐axis, then its radius should be expressed as a function of y. The volume ( V) of a solid generated by revolving the region bounded by y = f (x) and the x ‐axis on the interval [ a, b] about the x ‐axis is

How do you find the volume of a reel-shaped solid?

Find the volume of the reel-shaped solid formed by the revolution about the y -axis, of the part of the parabola y2 = 4 ax, cut off by the latus rectum. Solution. Let O be the vertex and L one extremity of the latus rectum of the given parabola y2 = 4 ax. For the arc OL, y varies from 0 to 2 a.

How to find the volume of an irregular shaped object?

Alternatively, you can find the volume of an irregular shaped object by applying the following steps: 1 First, break down the irregular solid into regular shapes whose volume can be calculated. 2 Calculate the partial volumes of the small shapes 3 Add up the partial volumes to get the total volume of the irregular shaped solid

How do you calculate the volume of a circular cylinder?

Circular Cylinder Volume 1 Volume = π r 2 h 2 Top Surface Area = π r 2 3 Bottom Surface Area = π r 2 4 Total Surface Area = L + T + B = 2 π rh + 2 ( π r 2) = 2 π r (h+r)

What is the volume of conical frustum?

Conical Frustum Volume Volume = (1/3)πh (r 1 2 + r 2 2 + (r 1 * r 2)) Lateral Surface Area Top Surface Area = πr 1 2 Base Surface Area = πr 2 2 Total Surface Area