### All Common Core: High School - Geometry Resources

## Example Questions

### Example Question #1 : Apply Density Concepts To Area And Volume Situations: Ccss.Math.Content.Hsg Mg.A.2

If a balloon is filled with cubic meters of xenon with a density of kilograms per cubic meter. How many kilograms of xenon does the balloon contain?

Round your answer to decimal places.

**Possible Answers:**

**Correct answer:**

In order to solve this problem, we need to use an equation that involves, density, mass, and volume. Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

### Example Question #1 : Apply Density Concepts To Area And Volume Situations: Ccss.Math.Content.Hsg Mg.A.2

If a balloon is filled with cubic meters of neon with a density of kilograms per cubic meter. How many kilograms of neon does the balloon contain?

Round your answer to decimal places.

**Possible Answers:**

**Correct answer:**

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

### Example Question #11 : Apply Density Concepts To Area And Volume Situations: Ccss.Math.Content.Hsg Mg.A.2

If a balloon is filled with cubic meters of water with a density of kilograms per cubic meter. How many kilograms of water does the balloon contain?

Round your answer to decimal places.

**Possible Answers:**

**Correct answer:**

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

### Example Question #12 : Apply Density Concepts To Area And Volume Situations: Ccss.Math.Content.Hsg Mg.A.2

If a balloon is filled with cubic meters of neon with a density of kilograms per cubic meter. How many kilograms of neon does the balloon contain?

Round your answer to decimal places.

**Possible Answers:**

**Correct answer:**

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Thus the mass of the balloon is .

### Example Question #1 : Geometric Methods To Solve Design Problems: Ccss.Math.Content.Hsg Mg.A.3

Suppose you have a 12ft x 12ft area that you want to lay down tile for. Your tiles are 2ft x 2ft each. How many tiles do you need to perform this task?

**Possible Answers:**

36 tiles

4 tiles

64 tiles

144 tiles

**Correct answer:**

36 tiles

When it comes to word problems such as these, always begin by drawing an illustration. Below is a picture of our 12 x 12 area we need to fill with tiles and one 2 x 2 tile that we are going to use to fill this area.

There are two methods that we can use to solve this problem:

Method 1:

First we need to ask, how many tiles are needed to line the width of this 12 x 12 area. So if we have tiles that are 2 ft each we need to divide 12 by 2 to figure out how many tiles we need to line the width.

And so we need 6 tiles to line the width.

No we need to ask, how many tiles are needed to line the height of this 12 x 12 area. So if we have tiles that are 2 ft each we need to divide 12 by 2 to figure out how many tiles we need to line the height.

And so we need 6 tiles to line the width.

Now we need to find the total amount of tiles needed to fill the entire 12 x 12 space. We can solve for this just like we solve for area. We will multiply the amount of tiles across the width by the amount of tiles lining the height. This gives us an “area” in terms of the amount of tiles needed to fill the space.

And so we need 36 tiles to fill the space

Method 2:

We begin by finding the area of the entire 12 x 12 space. We use the fact that

And so our area of the entire space is . Now we need to find the area of each individual tile.

And so the area of each individual tile is . To find the total amount of tiles needed we need to find the amount of sections in the total area. To do this we divide:

Our units of cancel and we are left with 36 tiles.

### Example Question #1 : Geometric Methods To Solve Design Problems: Ccss.Math.Content.Hsg Mg.A.3

You have a barrel (cylinder) that is 1ft in radius and 3 ft in height. There was a thunderstorm the night before and you have found that the barrel is full of water. How much water is in the barrel? Round to the second decimal

**Possible Answers:**

172.93L

266.74L

156.01L

9.42L

**Correct answer:**

266.74L

We must first recognize that this is a volume problem. There is a cylinder full of water and we must find the total volume of the cylinder in order to find the amount of water in the cylinder. We will use the formula for finding the volume of a cylinder, . is our radius and will be 1ft, is our height and will be 3ft.

But we cannot have represent volume. So we will use the conversion of cubic feet to liters. For every cubic foot there is 28.3168 liters.

Our units cancel and we are left with liters.

### Example Question #1 : Geometric Methods To Solve Design Problems: Ccss.Math.Content.Hsg Mg.A.3

You have been collecting stamps for a couple years now. You now think you have enough to decorate your right-angle triangular prism shaped jewelry box without leaving any open gaps. The triangular faces of your jewelry box have a height of 5in and a base length of 3in. The rectangular faces of your jewelry box have a height of 5in and a width of 7in. You have stamps that are each 1in x 1in squares. Do you have enough stamps?

**Possible Answers:**

No

Yes

There is not enough information

**Correct answer:**

No

The goal of this problem is to find the surface area of the triangular prism and see if you have enough 1in x 1in stamps to fill the surface area without leaving any open gaps. To find the surface area of the prism we know that there are two triangular faces, and three rectangular faces. We will find the area of each of these and then their sum is the total surface area.

Area for each triangular face:

Area for each rectangular face:

So now we will sum 2 triangular faces and three rectangular faces for the total surface area.

Since we want to find if we have enough stamps, we will divide the total surface area by the surface area of an individual stamp to find how many stamps we would need to cover the prism entirely.

We only have 112 stamps, so we do not have enough stamps.

### Example Question #1 : Geometric Methods To Solve Design Problems: Ccss.Math.Content.Hsg Mg.A.3

True or False: We want to find the amount of sod squares to lay within a fenced in area. This is a volume question.

**Possible Answers:**

True

False

**Correct answer:**

False

This is an area problem. For a fenced in, flat area, we would only consider the height and width. To be a volume problem we would need to have a 3-dimensional space to fill, one with width, length, and height.

### Example Question #1 : Geometric Methods To Solve Design Problems: Ccss.Math.Content.Hsg Mg.A.3

True or false: You want to find the radius of your water bottle. Assuming your water bottle is a cylinder and you know it holds 10oz of water, you are able to determine the radius.

**Possible Answers:**

False

True

### Example Question #1 : Geometric Methods To Solve Design Problems: Ccss.Math.Content.Hsg Mg.A.3

You would like to construct an open face rectangular prism to hold some garden plants. The prism is shown in the figure below. If the entire prism will be filled with potting soil, how much potting soil will you need?

**Possible Answers:**

18.75ft^{3}

12.5ft^{3}

17.25ft^{3}

9ft^{3}

**Correct answer:**

18.75ft^{3}

We need to understand that this is a volume question. We are trying to find the total volume of potting soil needed to fill this rectangular prism. The formula to find the volume of a rectangular prism is . The length of the prism is 5ft, the width of the prism is 1.5ft, and the height of the prism is 2.5. We will plug these into our formula to solve this problem.

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