# Common Core: High School - Geometry : Geometric Methods to Solve Design Problems: CCSS.Math.Content.HSG-MG.A.3

## Example Questions

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### 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 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 #2 : 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 #5 : 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 .

### 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 .

### 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 .

### Example Question #9 : 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 .

### Example Question #10 : 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 .