Video: Finding the Volume of a Pyramid

Determine, to the nearest tenth, the volume of the given solid.

01:40

Video Transcript

Determine, to the nearest tenth, the volume of the given solid.

Here, we have a pyramid, a triangular pyramid. And the formula for the area of a pyramid is one-third times the area of the base times the height. So this is a triangular pyramid because the base is a triangle. So the formula that we need to use for the area of the base would be one-half base times height. Now in the rest of the formula, there’s another height. But this is the height of the pyramid itself.

For a pyramid, the height will be perpendicular to the bottom, the base. So our height will be 14. So back to the area of the base, the area of the triangle, so when it says one-half base times height, that is the height of the triangle that’s on the bottom, the base. Since this is the right triangle, it won’t matter which leg we let be the base and which leg we let be the height.

So a little reminder, the side across from the right angle is the hypotenuse. And the other two sides we call legs. So it doesn’t matter which leg we wanna be the base and we would let be the height because it’s a right angle between them. So we will have one-half times 18 times 22. So now we need to simplify.

One-half times 18 is nine. And nine times 22 is 198. Multiplying all these together, we get 924. Now this is the volume. And it’s in centimeters. So it will be centimeters cubed. So the volume, to the nearest 10th, will be 924 cubic centimeters.

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