Geometry EOC Review 2026 tips #Geometry #eoc #florida #best#fast#Mathematics #mathshack

Added: 2026-05-09

[00:00:00]Welcome back to Delima's Concepts. In today's video, we're looking at some questions for our geometry EOC. So, let's take a look at this first question here. It says, "A cylinder is given. Identify the shape of a two-dimensional cross-section cut perpendicular to its base." So, perpendicular to its base, it means then we're going to be cutting it going down like this.

[00:00:26]Like you're going to slice it going down like that. And if we do so, definitely we will definitely see a rectangle if we cut it like that. We're going to see a rectangle, so that's a rectangle.

[00:00:43]Let's take a look for second question. A prism is given. Identify the shape of a two-dimensional cross-section cut parallel to its base. The base of a prism is named by its twin faces, right?

[00:01:00]So, this is a triangular prism. So, if we cut it parallel to the base, we're going to be cutting it like this, all right? Based on the orientation of this shape, and we would be seeing another triangle like this. You're going to see the same triangle that you're looking at here here again. So, definitely it is an acute it's an acute triangle that we're seeing, all right? We're seeing an acute triangle, meaning we're seeing this same triangle is going to be popping up back again, all right? Now, let's take a look at our third question.

[00:01:44]Take a look at the third question here.

[00:01:47]Question three.

[00:01:49]A prism is given. Identify the shape of a two-dimensional cross-section cut perpendicular to its base. So, we're going to go perpendicular to its base, that mean we're going to be cutting it like this going down like that. But when you do this, you're definitely going to see that rectangle on the inside again.

[00:02:11]So, this is a rectangle right there when we do cut it perpendicular to its base, all right?

[00:02:20]Now, number four says, "A cone is given.

[00:02:24]Identify the shape of a two-dimensional cross-section cut parallel to its base." We're going to be cutting it parallel to its base, that mean when we cut it parallel to its base, we're basically seeing a circle again.

[00:02:39]And if we keep cutting it, we'll see smaller circles. And this parallel to its base right here. All right? So, definitely we'll be seeing a circle for that.

[00:02:52]Now, we're looking at solids of rotation. Let's take a look at question five. It says here, "A right triangle is shown.

[00:03:00]Identify the three-dimensional object that will be generated by rotating the right triangle about the line M." So, this is suggesting that we're going to be going around M like that.

[00:03:16]Now, what we normally do for solids of rotation is to do a quick reflection across the line, so it would have been reflected across this line. We're seeing this.

[00:03:26]And then we're going to imagine that this is going to go around that axis. So, you could see the shape being formed when we do it. So, it's going to be B, all right? So, that is going to be B right there. Let's take a look at our number six.

[00:03:43]For number six, a rectangle is shown on the coordinate plane. Identify the three-dimensional object that will generate or will be generated by rotating the rectangle about the Y axis.

[00:04:00]Now, we're going to go This is our Y axis, as you all know. So, we're going to be going around the Y axis.

[00:04:08]So, we're going to be going around this axis like this. So, let me quickly do what I normally do. I normally do a reflection so I could see how far I'll go. So, this point will be here, and this point will be here. Okay? Now, if I just quickly just shape out a quick reflection across the axis, then we're referring to that's what This is going to be the boundaries for me. And then for each point, I'm going to just go around in a circle.

[00:04:42]So, imagine that we have a circle here.

[00:04:44]And imagine that we do another circle here.

[00:04:47]And whatever shape you see, that is the shape that will be formed from that. So, I'm seeing here that I do have a cylinder with a radius of three and the height of 1 2 3 4, right? So, a radius of three, height of four. Cylinder with a radius of three and height four. This is the answer. All right? So, basically we could look, see what's going on, and pick number seven. We're still rotating. It says, "A rectangle is shown on the coordinate plane.

[00:05:25]Which real-world object could be used to describe the figure created by rotating the rectangle about the Y axis?"

[00:05:36]So, again, I'm going to quickly do a reflection. So, this shape, as you could see, it's three units and four three to four units away from the Y axis, so it's going to fall somewhere over here if I reflect it.

[00:05:55]It's going to fall somewhere over here.

[00:05:57]Okay?

[00:05:59]So, let me just fix this up a little bit.

[00:06:04]And then we're going to have each point going around in a circle. So, this will give me a circle right here.

[00:06:14]This will give me a circle as well.

[00:06:20]Down here, I'm going to have the same.

[00:06:23]I'll have a whole circle there.

[00:06:26]And right here, we're going to have a circle again for the smaller version.

[00:06:29]So, basically when you see this, you're basically seeing uh I'm seeing a piece of plastic hose because in reality, I'm seeing something like this where this is going on, this is going on, and then we have a hole we have a hole in the middle of it right there. That's what we actually have. So, a plastic tube would be right for this. And the thing is because the plane shape was not touching the axis, it's going to create a hole in the center as you rotate. So, B is the correct answer for that. Let's take a look at question eight.

[00:07:12]Question eight says, "A circle is shown on the coordinate plane.

[00:07:16]Which real-world object could be used to describe the figure by rotating the circle about the X axis?" So, this is Y axis, this is my X axis. I'm going to rotate around the X axis, okay? But here's the thing. Basically, this X axis cut through the circle at its diameter.

[00:07:38]All right. So, what happened is when we rotate a circle around an axis where the circle is actually touching the axis or the axis is passing through the center, we're going to get a sphere, all right?

[00:07:53]Which will be represented like a basketball. So, not a donut, not an egg, not a piece of tube, I'm going to get a basketball. This is going to be a sphere as we rotate it around the axis.

[00:08:06]Remember that the axis passed through the center of the circle, and that would have made there is no opening for this.

[00:08:15]So, B is the answer.

[00:08:17]Let's take a quick look on um the area of two dimension. Now, we're looking at population density. It says the the state of North Dakota is shaped approximately like a rectangle, so we see North Dakota right there with a base of 300 miles and a height of 231 miles. If the current population is 796,570, which equation could be used for the population density? So, population density would be your size of your population divided by the area. So, area So, basically then we're saying this is a 305 by 231. So, the area of this rectangular thing would be multiplying these for the bottom. So, the area would be at the bottom. So, this would have been the idea where this is the population size, and we're dividing it by the area of North Dakota. So, our answer is A.

[00:09:24]Let's take a look at number 10.

[00:09:26]So, for number 10, um we have Broward County, um Florida, is approximately the shape of a rectangle, all right? So, we're looking at it right here.

[00:09:37]With a base of 48.32 and a height of 27.38.

[00:09:48]What is the population density if we have 1,978,170 people? So, the idea remained the same that our population density will be equal to the size of the population.

[00:10:08]And we're going to divide this by the area of the state. So, basically all we're going to do is to work this out 495.21.

[00:10:27]So, basically they want us to do this to the nearest whole number, so it's going to be 149 5. All right? And that's what we're really dealing with right there. That's the number we're looking for. All right?

[00:10:42]All right, let us take a look at the other question right here next door. So, in this case what we're dealing with is the Florida wildlife control, right? So, we have It looks this is It looks like a trapezoid.

[00:10:57]Um in the current population we have 658 panther. So, basically I need to find the area of this trapezoid. But when I look at it, um what I'm noticing is that some of the information is missing, so I'm going to have to furnish this to get all my information out, right? For example, um this spot right here is missing. So, this 31 here will be represented this 3.1 up there will be represented down here as well. So, if I should add 3.1 two times and then add it to 4.6, it's going to tell me that this base down here, I could call it base two, is actually 10.8.

[00:11:44]Now, in order to work this out, I definitely need the area of this trapezoid. So, the area of the trapezoid will equal to a half times its height times base one plus base two.

[00:12:05]So, we're just going to put these on our our calculator, okay?

[00:12:08]Oh, we're getting some 43.0 9. So, this is the area in kilometers, so square kilometers. Now, at the end of the day, if we want to know the population density of the panthers, we need to know how many panthers we have, which is 658.

[00:12:27]So, basically now the population density of those panthers will be the number of panthers, which is going to be 658, and we're going to divide this by 43.09.

[00:12:41]So, let us work this out. 658 divide by 43.09, and we're getting 15.27.

[00:12:52]But the question says to the nearest whole number, so this is approximately 15. So, this is the answer to the question. Thank you for watching Daily Math Content, and see you next time when we'll be looking at some more geometry videos. Bye-bye.