# Common Core: 7th Grade Math : Solve Problems Involving Area, Volume and Surface Area of Two- and Three-Dimensional Objects: CCSS.Math.Content.7.G.B.6

## Example Questions

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### Example Question #1 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

The length of the side of a cube is . Give its surface area in terms of .

Explanation:

Substitute  in the formula for the surface area of a cube:

### Example Question #1 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

If a cube has one side measuring cm, what is the surface area of the cube?

Explanation:

To find the surface area of a cube, use the formula , where represents the length of the side.  Since the side of the cube measures , we can substitute in for .

### Example Question #51 : Volume

If a cube is inches tall, what is its volume?

Not enough information provided.

Explanation:

To find the volume of a cube, we multiply length by width by height, which can be represented with the forumla .  Since a cube has equal sides, we can use for all three values.

### Example Question #1 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

What is the volume of a cube with a side length equal to  inches?

Explanation:

The volume of a a cube (or rectangular prism) can be solved using the following equation:

### Example Question #1 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

Give the volume of a cube with surface area 150 square inches.

Explanation:

Let  be the length of one edge of the cube. Since its surface area is 150 square inches, one face has one-sixth of this area, or  square inches. Therefore, , and .

The volume is the cube of this, or  cubic inches.

### Example Question #1 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

Give the volume of a cube with surface area 240 square inches.

Explanation:

Let  be the length of one edge of the cube. Since its surface area is 240 square inches, one face has one-sixth of this area, or  square inches. Therefore, , and .

The volume is the cube of this, or  cubic inches.

### Example Question #1 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

Find the surface area of a non-cubic prism with the following measurements:

Explanation:

The surface area of a non-cubic prism can be determined using the equation:

### Example Question #1 : How To Find The Surface Area Of A Prism

A small rectangular jewelry box has two square ends with areas of 36 square centimeters, and a width of 10 centimeters.  What is the surface area of the outside of the jewelry box.

Explanation:

To find the surface area of the rectangular box we just need to add up the areas of all six sides. We know that two of the sides are 36 square centimeters, that means we need to find the areas of the four mising sides. To find the area of the missing sides we can just multiply the side of one of the squares (6 cm) by the width of the box:

But remember we have four of these rectangular sides:

Now we just add the two square sides and four rectangular sides to find the total surface area of the jewelry box:

That is the total surface area!

### Example Question #1 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

Alice is wrapping a rectangular box that measures .  How many square feet of wrapping paper does she need?

Explanation:

The surface area of a rectangular prism is given by

where is the length, is the width, and is the height.

Let , , and

So the equation to solve becomes  or

However the question asks for an answer in square feet.  Knowing that  we can convert square inches to square feet.  It will take  of paper to wrap the present.

### Example Question #1 : Solve Problems Involving Area, Volume And Surface Area Of Two And Three Dimensional Objects: Ccss.Math.Content.7.G.B.6

An aquarium is shaped like a perfect cube; the perimeter of each glass face is  meters. If it is filled to the recommended  capacity, then, to the nearest hundred cubic liters, how much water will it contain?

Insufficient information is given to answer the question.

Note:

Explanation:

A perfect cube has square faces; if a face has perimeter  meters, then each side of each face measures one fourth of this, or  meters. The volume of the tank is the cube of this, or

cubic meters.

Its capacity in liters is  liters.

of this is

liters.

This rounds to liters, the correct response.

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