Question

Find the volume of the solid whose base is the unit circle, and whose cross-sections perpendicular to the x-axis are rectangles whose bases (on the xy-plane) are three times smaller than their heights

Answer 1

The volume of the solid (cylinder) is 6π unit³,

Volume

The volume of an object is the amount of space occupied by a three dimensional object.

A solid with a circular base and a vertical cross section is a cylinder.

Therefore the solid shown in the problem above is a cylinder.

A unit circle has a radius of 1, hence the radius of the cylinder = 1 unit, diameter = 2 * radius = 2 * 1 = 2 unit

Height of cylinder = 3 * diameter = 3 * 2 = 6 unit

Volume of cylinder = π * radius² * height = π * 1² * 6 = 6π unit³

The volume of the solid (cylinder) is 6π unit³.

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