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

## Example Questions

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### Example Question #7 : 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 511 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 85.16666666666667 for .

So the final answer is.

### Example Question #8 : 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 520 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 86.66666666666667 for .

So the final answer is.

### 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 897 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 149.5 for .

So the final answer is.

### 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 800 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 133.33333333333334 for .

So the final answer is.

### Example Question #11 : 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 738 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 123.0 for .

So the final answer is.

### Example Question #12 : 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  is the width and  volume.

Now plug in 154.16666666666666 for .

So the final answer is.

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