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Chapter 6

Test Yourself

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So this one says the figure above shows a solid formed by placing a CE atmosphere of radius three centimeters onto a cylinder whose height is six centimeters and whose radius is pre centimeters. What is the total volume in cubic inches of solid? Okay, so for this one, it's important to realize that we've got to figure is going on here. Got it, cylinder. And we've got this part, which is actually just half of a sphere. Let's go out and get the equations for the half of the sphere and the cylinder. So for a sphere just a regular sphere, we know it's going to be four thirds. Pi are cute, but again, this one is only half the spirits. So we're going to multiply this entire equation. I want half. So then, for the volume of a cylinder, we know that it's just gonna be pi r squared h. So then let's go ahead and fill in what we know so far, The radius. We know it's three, so this one is going to be V is equal to one half times for over three pie times three Cute, which is going to simplify Teo to over three pi times twenty seven and then if we simplify that, we would get eighteen pie. So the volume of this, uh, half sphere up here there's going to be eighteen pipes. So then let's get the volume of a cylinder. So we know that the is equal to pi times R squared, which is still a three temps of H, which is the six from this implied simplifies to V is equal to pi times nine times six, which is fifty four. So then this much right here, this inside is going to be fifty four pi. So then, if we want the total volume, all we have to do is add those two things. We have fifty four pi plus eighteen pie, which is going to give us seventy two by so see is our answer.

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