 Number 10 we're finding the exact volume of two cones that have been put together at their bases So what we're gonna do here is we're going to add together the volume of the two cones So volume of the first cone Which you can't really read what that says Okay, so a volume of the first cone plus Volume of the second cone when we add those together it'll give us the volume of that whole figure All right, so volume of a cone is one third times pi r squared times the height of the cone and Same thing for the other cone You'll see that the radius is the same for both cones The only thing that's different is the height so for the first one. I'm gonna do one third times pi times 7.5 squared times four and for the second one. It's gonna be exactly the same thing 7.5 squared, but the height is 10 Now it does say give the exact volume So you're gonna start with this right here and calculate 7.5 squared times 4 divide that by 3 you should get 75. So that's 75 pi when you do this Evaluation 7.5 squared times 10 divided by 3 you get 187.5 pi and Then when you add those two together You get 262 oops 0.5 pi and that is centimeters cubed so 262.5 cubic centimeters would be the total volume of this shape in number 11 We're gonna find the volume of a hexagonal prism if all the edges are 10 inches key word here is all What that means is that not only are the edges of the hexagon 10 But the height of the prism would also be 10 Again, the other thing you want to keep in mind here is we're doing a prism not a pyramid So the volume is going to be the area of the base times the height and because the base is a Hexagon we're gonna do one half times a Pothim times perimeter and We're gonna have to then use Our hexagon Excuse my terrible drawing and Find the apothem. So this is a Because the side length is 10 this is 5 if we find the central angle 360 divided by 6 is 60 degrees. So we know that this is a 30 60 90 triangle therefore the apothem has to be 5 root 3 and The perimeter since all the sides are 10 and there are six sides the perimeter is 60 So one half times 5 root 3 times 60 times the height of the prism which is 10 because again remember if all of the edges are 10 That means that in the pentagon. I'm sorry the hexagon and the prism Would have a height of 10 So now if I multiply through I get 1500 root 3 and that would be cubic inches