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High School Math : Cubes

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

If the surface area of a cube equals 96, what is the length of one side of the cube?

Possible Answers:

Correct answer:

Explanation:

The surface area of a cube = 6a² where a is the length of the side of each edge of the cube. Put another way, since all sides of a cube are equal, a is just the lenght of one side of a cube.

We have 96 = 6a²→ a² = 16, so that's the area of one face of the cube.

Solving we get √16, so a = 4

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

What is the surface area of a cube with a side length of s=7.2in ?

Possible Answers:

$311in^{2}$

$373in^{2}$

$52in^{2}$

$331in^{2}$

$86in^{2}$

Correct answer:

$311in^{2}$

Explanation:

In order to find the surface area of a cube, use the formula $SA=6(s^{2})$ .

$SA=6*(7.2in)^{2}$

$SA=6*51.84in^{2}$

$SA=311.04in^{2}$

$\rightarrow 311in^{2}$

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

What is the surface area, in inches, of a rectangular prism with a length of $\dpi{100} l=2.2ft$ , a width of w=18in , and a height of h=14in ?

Possible Answers:

$2193.6in^{2}$

$6652.8in^{2}$

$1108.8in^{2}$

$2652.8in^{2}$

$2319in^{2}$

Correct answer:

$2193.6in^{2}$

Explanation:

In order to find the surface area of a rectangular prism, use the formula SA=(2*lw)+(2*wh)+(2*lh) .

However, all units must be the same. All of the units of this problem are in inches with the exception of $\dpi{100} l=2.2ft$ .

Convert to inches.

$l=\frac{2.2ft}{1}*\frac{12in}{1ft}$

l=26.4in

Now, we can insert the known values into the surface area formula in order to calulate the surface area of the rectangular prism.

SA=(2*26.4in*18in)+(2*18in*14in)+(2*26.4in*14in)

$SA=(950.4in^{2})+(504in^{2})+(739.2in^{2})$

$SA=2193.6in^{2}$

If you calculated the surface area to equal $6652.8in^{2}$ , then you utilized the volume formula of a rectangular prism, which is V=l*w*h ; this is incorrect.

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

Square_with_diagonal What is the surface area of a cube with a diagonal of $\dpi{100} d=4.2cm$ ?

Possible Answers:

$42.22cm^{2}$

$59.22cm^{2}$

$52.92cm^{2}$

$105.84cm^{2}$

$84.05cm^{2}$

Correct answer:

$52.92cm^{2}$

Explanation:

A few facts need to be known to solve this problem. Observe that the diagonal of the square face of the cube cuts it into two right isosceles triangles; therefore, the length of a side of the square to its diagonal is the same as an isosceles right triangle's leg to its hypotenuse: $1:\sqrt{2}$ .

$\frac{s}{d}=\frac{1}{\sqrt{2}}$

$\dpi{100} \dpi{100} \frac{s}{4.2cm}=\frac{1}{\sqrt{2}}$

Rearrange an solve for .

$\dpi{100} s=\frac{4.2cm}{\sqrt{2}}$

Now, solve for the area of the cube using the formula $\dpi{100} \dpi{100} SA=6(s^{2})$ .

$SA=6*(\frac{4.2cm}{\sqrt{2}})^{2}$

$SA=\frac{6}{1}*(\frac{4.2cm}{\sqrt{2}}*\frac{4.2cm}{\sqrt{2}})$

$\dpi{100} SA=\frac{6}{1}*(\frac{17.64cm^{2}}{2})$

$\dpi{100} \dpi{100} SA=3*17.64cm^{2}$

$\rightarrow 52.92cm^{2}$

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

This figure is a cube with one face having an area of 16 in². Cube

What is the surface area of the cube (in²)?

Possible Answers:

256

Correct answer:

Explanation:

The surface area of a cube is the sum of the area of each face. Since there are 6 faces on a cube, the surface area of the entire cube is $6\cdot16$ .

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Example Question #11 : Cubes

A cube has a height of 4 feet. What is the surface area of the cube in feet?

Possible Answers:

Correct answer:

Explanation:

To find the surface area of a cube, square the length of one edge and multiply the result by six: $6(a^{2})$

$6(4^{2})=6(16)=96$

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Example Question #9 : How To Find The Surface Area Of A Cube

The side length of a particular cube is $\frac{3}{2}$ . What is the surface area of this cube?

Possible Answers:

$\frac{9}{2}$

$\frac{27}{2}$

Correct answer:

$\frac{27}{2}$

Explanation:

To find the surface of a cube, use the standard equation:

SA=6a^2

where denotes the side length.

Plug in the given value for to find the answer:

$SA=6\cdot \left(\frac{3}{2}\right)^2=6\cdot \left(\frac{9}{4}\right)=\frac{27}{2}$

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Example Question #10 : How To Find The Surface Area Of A Cube

Sarah is wrapping a birthday present. The box is a cube with sides of $6\; in$ . At a minimum, how many square feet of wrapping paper will she need?

Possible Answers:

$1.00\; ft^{2}$

$0.50\; ft^{2}$

$1.50\; ft^{2}$

$0.75\; ft^{2}$

$1.25\; ft^{2}$

Correct answer:

$1.50\; ft^{2}$

Explanation:

Remember, $6\; in=0.50\; ft$ .

For a cube:

$SA = 6s^{2}$

Thus $6(0.50)^{2}=6(0.25)=1.50\; ft^{2}$ .

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Example Question #11 : Cubes

$\textup{What is the surface area, in terms of }p,\textup{of a cube with sides of length }p\textup{ ?}$

Possible Answers:

12p

$p^{2}$

$4p^{2}$

$p^{3}$

$6p^{2}$

Correct answer:

$6p^{2}$

Explanation:

$\textup{Each of the six identical faces of the cube is a square with sides }p.$

$\textup{Each face: }A=p^{2}\: \: \: \: \: \textup{Surface area}=6p^{2}$

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Example Question #581 : Geometry

Find the surface area of the following cube:

Length_of_diagonal

Possible Answers:

$80\ m^2$

$96\ m^2$

$90\ m^2$

$82\ m^2$

$88\ m^2$

Correct answer:

$96\ m^2$

Explanation:

The formula for the surface area of a cube is

SA=6(s)^2 ,

where is the length of the side.

Plugging in our values, we get:

$SA=6(4\ m)^2$

$SA=96\ m^2$

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High School Math : Cubes

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

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

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

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

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

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

Example Question #11 : Cubes

Example Question #9 : How To Find The Surface Area Of A Cube

Example Question #10 : How To Find The Surface Area Of A Cube

Example Question #11 : Cubes

Example Question #581 : Geometry

All High School Math Resources

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