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Find the volume of the solid shown at the right.

a. Use the formula for the volume of a _____$$V=\frac{1}{3} s^{2} h$$

b. Replace $s$ by _____ and $h$ by _____$$V=\frac{1}{3}(\quad)^{2}(\quad)$$

c. Multiply. $$V=\frac{1}{3}(\quad)(7)=(\quad)(7)=$$

d. Fill in the blank with the correct unit: The volume of the pyramid is 84 _______.

An Introduction to Geometry

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this problem is sort of like a guided practice. And what it's gonna allow me to dio is determine the steps for going through figuring out the volume of a solid. So I have reconstructed this drawing here with the square pyramid. I know it's square pyramid because it comes to a point at the top and it is a square base. It and I know it's a square because it has two measurements here on the length and the width other six centimeters of in a square. Pearman on. And that is the answer for a give us the volume formula. And this is the volume formula for a square pyramid. And the square pyramid really just comes into play here with this s square because normally with volume, we use the capital B to represent the area of the base. But because this is a square base, we can just say that it's the sides square. All right, so then be it wants us to put in the actual values. So we're gonna replace the S for the side is going to be calm six centimeters, because those are the sides of the base. That's what we're talking about when we say sides, it's the base and the height is going to become seven centimeters. So we replace this in the formula, we substitute it, it becomes 1/3. Ah, six squared times sudden and now see tells us to do that actual math. So we have. First we're going to dio are parentheses or exponents of exponents, which is six squared. So six squared is 36. And so that's how I went from this to this. And then from here to here, I'm doing 1/3 of 36. That's because I'm going multiplying from left to right. And so 1/3 of 36 is 12. And so from here, do you hear? I did one sir of 36 and now I'm gonna dio 12 times seven, which is 80 for its anymore. Oh, it's break here. Okay, just a all right, though that is the work. First step. See on then. We have 84 and it wants us to have the units. Of course, we always want units from where cocky but measurement. Otherwise we don't know what it is. The 84 puppies, I don't know, but here it's not 84 puppies. It is centimeters. And because this is a three dimensional measurement, volume is three dimensional. It is Shoob. This is 84 cubic centimeters.

Ohio State University

An Introduction to Geometry