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High School Math : How to find the surface area of a cube

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

The side of a cube has a length of $\dpi{100} \small 5 cm$ . What is the total surface area of the cube?

Possible Answers:

$\dpi{100} \small 5cm^{2}$

$\dpi{100} \small 150cm^{2}$

$\dpi{100} \small 50 cm^{2}$

$\dpi{100} \small 25 cm^{2}$

$\dpi{100} \small 125 cm^{2}$

Correct answer:

$\dpi{100} \small 150cm^{2}$

Explanation:

A cube has 6 faces. The area of each face is found by squaring the length of the side.

$\dpi{100} \small 5\times 5 = 25$

Multiply the area of one face by the number of faces to get the total surface area of the cube.

$\dpi{100} \small 25 \times 6=150$

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

What is the surface area of a cube if its height is 3 cm?

Possible Answers:

$45\ cm^2$

$63\ cm^2$

$36\ cm^2$

$54\ cm^2$

$25\ cm^2$

Correct answer:

$54\ cm^2$

Explanation:

The area of one face is given by the length of a side squared.

$A_{face}=(3cm)^2=9\ cm^2$

The area of 6 faces is then given by six times the area of one face: 54 cm².

$A_{total}=6(A_{face})=6(9\ cm^2)=54\ cm^2$

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

A sphere with a volume of $\frac{32}{3}$ $\pi m^{3}$ is inscribed in a cube, as shown in the diagram below.

Act4

What is the surface area of the cube, in $m^{2}$ ?

Possible Answers:

$48\pi \ m^{2}$

$96\ m^{2}$

$24\ m^{2}$

$48\ m^{2}$

$48\pi ^{2}\ m^{2}$

Correct answer:

$96\ m^{2}$

Explanation:

We must first find the radius of the sphere in order to solve this problem. Since we already know the volume, we will use the volume formula to do this.

$V_{sphere}=\frac{4}{3}\pi r^{3}$

$\frac{32}{3}\pi =\frac{4}{3}\pi r^{3}$

$\frac{32}{3}=\frac{4}{3}r^{3}$

$\frac{3}{4}\cdot \frac{32}{3}= r^{3}$

$8=r^{3}$

r=2

With the radius of the sphere in hand, we can now apply it to the cube. The radius of the sphere is half the distance from the top to the bottom of the cube (or half the distance from one side to another). Therefore, the radius represents half of a side length of a square. So in this case

$side=2\cdot 2=4$

The formula for the surface area of a cube is:

$SA_{cube}=6s^{2}$

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

The surface area of the cube is $96\ m^{2}$

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Example Question #11 : How To Find The Surface Area Of A Cube

If a right triangle has a hypotenuse of length 5, and the length of the other sides are and , what would be the surface area of a cube having side length ?

Possible Answers:

$5\sqrt{5}$

None of these answers.

$25\sqrt{5}$

Correct answer:

Explanation:

By the Pythagorean Theorem,

x^2 + (2x)^2 = 5^2

x^2 + 4x^2 = 25

5x^2 = 25

x^2 = 5

$x=\sqrt{5}$

The surface area of a cube having 6 sides, is 6 times the area of one of its sides.

The area of any side of a cube is the square of the side length.

So if the side length is , the area of any side is x^2 , or .

Thus the surface area of the cube is

6*(5)

=30

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High School Math : How to find the surface area of a cube

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #11 : Cubes

Example Question #581 : Geometry

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

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

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

Example Question #11 : How To Find The Surface Area Of A Cube

All High School Math Resources

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