A cylinder, sphere, pyramid cone and a cube are all geometric shapes, where specific formulas are given when calculating the volume. As long as you know the height and length of a side or the radius, you can easily calculate the volume. However, how do you calculate the shape of the object when it is no longer a cylinder, sphere, pyramid, cone or a cube?
The shape above resembles a cone, but is not exactly a cone. Thanks to mathematics, most volumes of a geometric shape can be calculated. Today, the focus is on shapes that were created by revolving a region in the plane about a line. The shape seen above can be created when y=√x (x≤4) is revolved around the x-axis (green line). The formula used for calculating the volume when revolved around the x axis is:
Using the equation y=√x (x≤4) , the lower boundary a is 0, and the higher boundary b is 4. Now let’s substitute
into the formula. Then we integrate and simply find the volume
When the function gets complex, determining the volume could get challenging, because the integration process becomes intricate. However, the formula from above can always be used to calculate the volume when revolving a function/region around the x-axis. Try it yourself!
Works Cited
“Volume of a Solid of Revolution: Disks and Washers.” Math24.net, 2024,
math24.net/volume-solid-of-revolution-disks-washers.html. Accessed 5 Aug. 2024
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