Posts tagged volume
Finding volume over Type I and Type II regions

We already know that we can use double integrals to find the volume below a surface over some region R=[a,b]x[c,d]. We can define the region R as Type I, Type II, or a mix of both. Type I curves are curves that can be defined for y in terms of x and lie more or less “above and below” each other. On the other hand, Type II curves are curves that can be defined for x in terms of y and lie more or less “left and right” of each other.

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Using a double integral to find the volume of an object

We already know that we can use double integrals to find the volume below a function over some region given by R=[a,b]x[c,d]. We use the double integral formula V=int int_D f(x,y) dA to find volume, where D represents the region over which we’re integrating, and f(x,y) is the curve below which we want to find volume.

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Finding the volume and surface area of a sphere

In this lesson we’ll look at the volume and surface area of spheres. A sphere is a perfectly round ball; it’s the three-dimensional version of a circle. There are specific formulas we need to use to find the volume of a sphere and the surface area of a sphere.

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Theorem of Pappus to find volume using the centroid

The Theorem of Pappus tells us that the volume of a three-dimensional solid object that’s created by rotating a two-dimensional shape around an axis is given by V=Ad. V is the volume of the three-dimensional object, A is the area of the two-dimensional figure being revolved, and d is the distance traveled by the centroid of the two-dimensional figure.

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