ISEE Upper Level Quantitative Reasoning - How to find the surface area of a cube

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 $6s^{2}$ , where represents the length of the side. Since the side of the cube measures , we can substitute in for .

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

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

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

$6x^{2} -10x + 25$

$6x^{2} -60x - 150$

Explanation

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

$A = 6s^{2}$

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

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

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

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

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:

$SA_{cube}=6s^2$

Plug in our side length to find our answer:

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

Making our answer:

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

$486\text{cm}^2$

$324\text{cm}^2$

$218\text{cm}^2$

$576\text{cm}^2$

$338\text{cm}^2$

Explanation

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

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

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

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

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

$216\text{in}^2$

$27\text{in}^2$

$144\text{in}^2$

$72\text{in}^2$

$432\text{in}^2$

Explanation

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

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

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

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

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

$96\text{cm}^2$

$64\text{cm}^2$

$48\text{cm}^2$

$24\text{cm}^2$

$128\text{cm}^2$

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

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

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

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

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

$294\text{in}^2$

$343\text{in}^2$

$84\text{in}^2$

$147\text{in}^2$

$245\text{in}^2$

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 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

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

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

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

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?

Explanation

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: