# Common Core: High School - Geometry : Modeling with Geometry

## Example Questions

### Example Question #7 : 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?

Explanation:

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 #8 : 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?

Explanation:

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

Explanation:

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 #461 : High School: Geometry

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?

Explanation:

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 #461 : High School: Geometry

Find the volume of a cube, if its surface area is .

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where  is surface area and l is the length.

Now we plug 539 for  and solve for .

Now since we have the width, we can plug it into the volume formula, which is

Where w is the width and V volume.

Now plug in  for .

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

Find the volume of a cube, if its surface area is .

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where  is surface area and  is the length.

Now we plug 715 for  and solve for .

Now since we have the width, we can plug it into the volume formula, which is

Where  is the width and  volume.

Now plug in 119.16666666666667 for .

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

Find the volume of a cube, if its surface area is .

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where  is surface area and  is the length.

Now we plug 925 for  and solve for .

Now since we have the width, we can plug it into the volume formula, which is

Where w is the width and  volume.

Now plug in 154.16666666666666 for .

### Example Question #4 : Geometric Methods To Solve Design Problems: Ccss.Math.Content.Hsg Mg.A.3

Find the volume of a cube, if its surface area is .

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where  is surface area and  is the length.

Now we plug 729 for  and solve for .

Now since we have the width, we can plug it into the volume formula, which is

Where  is the width and  volume.

Now plug in 121.5 for .

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

Find the volume of a cube, if its surface area is .

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where  is surface area and  is the length.

Now we plug 584 for  and solve for .

Now since we have the width, we can plug it into the volume formula, which is

Where  is the width and  volume.

Now plug in 97.33333333333333 for .

### Example Question #6 : Geometric Methods To Solve Design Problems: Ccss.Math.Content.Hsg Mg.A.3

Find the volume of a cube, if its surface area is .

Explanation:

In order to find the volume, we need to remember the equation that involves both surface area, and volume.

Where  is surface area and  is the length.

Now we plug 744 for  and solve for .

Now since we have the width, we can plug it into the volume formula, which is

Where  is the width and  volume.

Now plug in 124.0 for .