How to find the surface area of a cube - ISEE Upper Level Mathematics Achievement

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Question

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

Answer

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

$A = 6s^{2}$

$A = 6 \left ( x - 5\right )^{2}$

$A = 6 \left ( x^{2} - 2 \cdot 5 \cdot x + 5^{2}\right )$

$A = 6 \left ( x^{2} - 10x +25\right )$

$A = 6 x^{2} - 60x +150$

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Question

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

Answer

To find the surface area of a cube, use the formula $6s^{2}$ , where represents the length of the side. Since the side of the cube measures , we can substitute in for .

$6(4)^{2}=96: cm^{2}$

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Question

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?

Answer

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:

$SA_{cube}=6s^2$

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

Plug in our known to get our answer:

$SA_{cube}=6(5cm)^2=6*25cm^2=150cm^2$

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Question

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

Answer

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:

$SA_{cube}=6s^2$

Plug in our side length to find our answer:

$SA_{cube}=6(9mm)^2=6*81mm^2=486mm^2$

Making our answer:

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Question

One of your holiday gifts is wrapped in a cube-shaped box.

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

Answer

One of your holiday gifts is wrapped in a cube-shaped box.

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.

$SA_{square}=6s^2=6(6in)^2=216in^2$

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Question

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

Answer

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

$SA = 6 \cdot (6\text{cm})^2$

$SA = 6 \cdot 36\text{cm}^2$

$SA = 216\text{cm}^2$

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Question

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

Answer

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

$SA = 6 \cdot (7\text{in})^2$

$SA = 6 \cdot 49\text{in}^2$

$SA = 294\text{in}^2$

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Question

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

Answer

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

$SA = 6 \cdot (4\text{in})^2$

$SA = 6 \cdot 16\text{in}^2$

$SA = 96\text{in}^2$

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Question

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

Answer

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

$SA = 6 \cdot l \cdot w$

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

$SA = 6 \cdot 12\text{in} \cdot 12\text{in}$

$SA = 6 \cdot 144\text{in}^2$

$SA = 864\text{in}^2$

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Question

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

Answer

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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Question

Find the surface area of a cube with a base of 8in.

Answer

A cube has all equal sides (length, width, height). To find the surface area of a cube, we will use the following formula:

Now, we know the base of the cube is 8in. Because all sides are equal (i.e. all sides are 8in), we will use that to substitute into the formula. We get

$SA = 6 \cdot (8\text{in})^2$

$SA = 6 \cdot 64\text{in}^2$

$SA = 384\text{in}^2$

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Question

You are building a box to hold your collection of rare rocks. You want to build a cube-shaped box with a side length of 3 feet. If you do so, what will the surface area of your box be?

Answer

You are building a box to hold your collection of rare rocks. You want to build a cube-shaped box with a side length of 3 feet. If you do so, what will the surface area of your box be?

To find the surface area, use the formula:

Where s is our side length and SA is our surface area.

Plug in our known and simplify

So, our answer is

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Question

Find the surface area of a cube with a length of 11in.

Answer

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. Because it is a cube, all sides are equal. Therefore, we can use any side in the formula.

Now, we know the length of the cube is 11in. We can substitute that into the formula. We get

$SA = 6 \cdot (11\text{in})^2$

$SA = 6 \cdot 121\text{in}^2$

$SA = 726\text{in}^2$

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Question

Find the surface area of a cube with a width of 7cm.

Answer

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. We can use any side because all sides have the same length on a cube.

Now, we know the width of the cube is 7cm. So, we can substitute. We get

$SA = 6 \cdot (7\text{cm})^2$

$SA = 6 \cdot 49\text{cm}^2$

$SA = 294\text{cm}^2$

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Question

Find the surface area of a cube with a width of 6cm.

Answer

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.

So, we get

$SA = 6 \cdot (6\text{cm})^2$

$SA = 6 \cdot 6\text{cm}^2$

$SA = 216\text{cm}^2$

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Question

Find the surface area of a cube with a length of 9cm.

Answer

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

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

Now, we know the length of the cube is 9cm. So, we get

$SA = 6 \cdot (9\text{cm})^2$

$SA = 6 \cdot 81\text{cm}^2$

$SA = 486\text{cm}^2$

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Question

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

Answer

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 7in. Because it is a cube, all sides are equal (this is why we can use any length in the formula). So, we will use 7in in the formula. We get

$SA = 6 \cdot (7\text{in})^2$

$SA = 6 \cdot 49\text{in}^2$

$SA = 294\text{in}^2$

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Question

Find the surface area of a cube with a width of 6in.

Answer

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

$SA = 6 \cdot l \cdot w$

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

Now, we know the width of the cube is 6in. Because it is a cube, all lengths, widths, and heights are the same. Therefore, the length is also 6in.

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

$SA = 6 \cdot 6\text{in} \cdot 6\text{in}$

$SA = 6 \cdot 36\text{in}^2$

$SA = 216\text{in}^2$

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