ISEE Upper Level Math : How to find the surface area of a cube

Example Questions

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Example Question #1 : Solve For Surface Area

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 #1 : How To Find The Surface Area Of A Cube

Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5 cm, what is the surface area of the cube?

Explanation:

Your friend gives you a puzzle cube for your birthday. If the length of one edge is 5 cm, what is the surface area of the cube?

To find the surface area of a cube, use the following formula:

This works, because we have 6 sides, each of which has an area of

Plug in our known to get our answer:

Example Question #2 : How To Find The Surface Area Of A Cube

A cube has a side length of , what is the surface area of the cube?

Explanation:

A cube has a side length of , what is the surface area of the cube?

Surface area of a cube can be found as follows:

Plug in our side length to find our answer:

Example Question #3 : How To Find The Surface Area Of A Cube

If one of the edges has a length of 6 inches, what is the surface area of the box?

Explanation:

If one of the edges has a length of 6 inches, what is the surface area of the box?

We can find the surface area of a square by squaring the length of the side and then multiplying it by 6.

Example Question #4 : How To Find The Surface Area Of A Cube

Find the surface area of a cube that has a width of 6cm.

Explanation:

To find the surface area of a cube, we will use the following formula:

where a is the length of any side of the cube.

Now, we know the width of the cube is 6cm.  Because it is a cube, all sides are 6cm.  That is why we can choose any side to substitute into the formula.

Now, knowing this, we can substitute into the formula.  We get

Example Question #5 : How To Find The Surface Area Of A Cube

Find the surface area of a cube with a length of 7in.

Explanation:

To find the surface area of a cube, we will use the following formula:

where a is the length of any side of the cube.  Note that all sides are equal on a cube.  That is why we can use any length in the formula.

Now, we know the length of the cube is 7in.

Knowing this, we can substitute into the formula.  We get

Example Question #6 : How To Find The Surface Area Of A Cube

Find the surface area of a cube with a width of 4cm.

Explanation:

To find the surface area of a cube, we will use the following formula.

where a is the length of any side of the cube.

Now, we know the width of the cube is 4in.  Because it is a cube, all sides are equal (this is why we can use any length in the formula).  So, we will use 4in in the formula.  We get

Example Question #7 : How To Find The Surface Area Of A Cube

Find the surface area of a cube with a length of 12in.

Explanation:

To find the surface area of a cube, we will use the following formula:

where l is the length, and w is the width of the cube.

Now, we know the length of the cube is 12in.  Because it is a cube, all lengths, widths, and heights are the same.  Therefore, the width is also 12in.

Knowing this, we can substitute into the formula.  We get

Example Question #8 : How To Find The Surface Area Of A Cube

While exploring an ancient ruin, you discover a small puzzle cube. You measure the side length to be . Find the cube's surface area.

Explanation:

While exploring an ancient ruin, you discover a small puzzle cube. You measure the side length to be . Find the cube's surface area.

To find the surface area, use the following formula:

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