McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
6. Surface Areas and Volumes of Spheres
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Exercise 55 Page 887

What do you need to find the volume of a pyramid? What have you been given?

Practice makes perfect
The volume of a pyramid is one-third the product of the area of the base and the height.
Let's consider the given pyramid.

We know two sides of the base and we have been given a slant height. The given information is not sufficient to solve the problem. Therefore, we will also assume the pyramid has a base in the shape of a rectangle and that its height is in the center of the base.

Let's create a right triangle with the height as one of its sides and the slant height as the hypotenuse.

The right triangle has one side with a length of and a hypotenuse with a length of By using the Pythagorean Theorem we can find the pyramid's height,
Solve for
The height of a pyramid must be non-negative, which is why we only kept the principal root when solving the equation. Next we will use the formula for area of a rectangle to find the area of the base,
We can now calculate the volume of the pyramid.
The volume of the pyramid to the nearest tenth is