Call Now to Set Up Tutoring:

(888) 888-0446

ACT Math : Cubes

Study concepts, example questions & explanations for ACT Math

Create An Account

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #2 : 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

Report an Error

Example Question #651 : Geometry

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:

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

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

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

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

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

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.

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

Report an Error

Example Question #21 : Cubes

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

Possible Answers:

$63\ cm^2$

$36\ cm^2$

$45\ cm^2$

$54\ cm^2$

$25\ cm^2$

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.

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

Report an Error

Example Question #3 : 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:

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

$96\ m^{2}$

$48\pi \ m^{2}$

$24\ m^{2}$

$48\ m^{2}$

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 $96\ m^{2}$

Report an Error

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

What is the surface area, in square inches, of a four-inch cube?

Possible Answers:

$192\:in^2$

$24\:in^2$

$96\:in^2$

$64\:in^2$

$384\:in^2$

Correct answer:

$96\:in^2$

Explanation:

To answer this question, we need to find the surface area of a cube.

To do this, we must find the area of one face and multiply it by , because a cube has faces that are square in shape and equal in size.

To find the area of a square, you multiply its length by its width. (Note that the length and width of a square are the same.) Therefore, for this data:

$area = L\cdot W=4\:in\cdot 4\:in=16\:in^2$

We now must multiply the area of one face by 6 to get the total surface are of the cube.

$16\:in^2\cdot6=96\:in^2$

Therefore, the surface are of a four-inch cube is $96\:in^2$ .

Report an Error

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

What is the surface area of a cube with a volume of 512mm^3 ? Round your answer to the nearest hundreth if necessary

Possible Answers:

256mm^2

135.76mm^2

64mm^2

384mm^2

90.51mm^2

Correct answer:

384mm^2

Explanation:

First we need to find the side length of the cube. Do that by taking the cube root of the volume.

$\sqrt[n]{512mm^3}$ = 8mm
Next plug the side length into the formula for the surface area of a cube:

SA = 6*s^2 = 6 *(8mm)^2 = 384mm^2

Report an Error

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

What is the surface area, in square inches, of a cube with sides measuring 4 inches ?

Possible Answers:

64in^2

32in^2

16in^2

96in^2

12in^2

Correct answer:

96in^2

Explanation:

The surface area of a cube is a measure of the total area of the surface of all of the sides of that cube.

Since a cube contains square sides, the surface area is times the area of a square side.

The area of one square side is sidelength sidelength, or 4*4 = 16 in this case. Therefore, the surface area of this cube is 16*6 = 96 square inches.

Report an Error

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

What is the length of the side of a cube whose surface area is equal to its volume?

Possible Answers:

s = 10

s = 4

There is not enough information to determine the answer.

$s = \sqrt{6}$

s = 6

Correct answer:

s = 6

Explanation:

To find the side length of a cube whose surface area is the same as its volume, set the surface area and volume equations of a cube equal to each other, the solve for the side length:

V=s^3: SA=6a^2

Set these two formulas equal to eachother and solve for s.

$\\ s^3 = 6*s^2 \\ \newline \frac{s^3}{s^2}=\frac{6*s^2}{s^2}\\ \newline s = 6$

Report an Error

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

What is the surface area of a cube with a side of length $\textup{3ft}$ ?

Possible Answers:

$9\textup{ ft}^2$

$54\textup{ ft}^2$

$162\textup{ ft}^2$

$27\textup{ ft}^2$

$18\textup{ ft}^2$

Correct answer:

$54\textup{ ft}^2$

Explanation:

To find the surface area of a cube with a given side length, use the formula:
SA = 6s^2 = 6*3^2 = 6*9 = 54

Report an Error

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

Find the surface area of a cube whose side length is .

Possible Answers:

Correct answer:

Explanation:

To find surface area of a cube, simply calculate the area of one side and multiply it by . Thus,

SA=s^2*6=4^2*6=16*6=96

Report an Error

View ACT Math Tutors

Nate
Certified Tutor

University of Wisconsin-Oshkosh, non degree, Prepharmacy. University of Wisconsin-Madison, Pharmaceutical Chemist, Pharmacy.

View ACT Math Tutors

Sumit
Certified Tutor

Calcutta University, Bachelor of Science, Mathematics. Indian Statistical Institute, Master of Science, Mathematics.

View ACT Math Tutors

Jason
Certified Tutor

Brigham Young University, Bachelor, Neuroscience.

All ACT Math Resources

14 Diagnostic Tests 767 Practice Tests Question of the Day Flashcards Learn by Concept

ACT Math Tutors in Top Cities:

Atlanta ACT Math Tutors, Austin ACT Math Tutors, Boston ACT Math Tutors, Chicago ACT Math Tutors, Dallas Fort Worth ACT Math Tutors, Denver ACT Math Tutors, Houston ACT Math Tutors, Kansas City ACT Math Tutors, Los Angeles ACT Math Tutors, Miami ACT Math Tutors, New York City ACT Math Tutors, Philadelphia ACT Math Tutors, Phoenix ACT Math Tutors, San Diego ACT Math Tutors, San Francisco-Bay Area ACT Math Tutors, Seattle ACT Math Tutors, St. Louis ACT Math Tutors, Tucson ACT Math Tutors, Washington DC ACT Math Tutors

Popular Courses & Classes

MCAT Courses & Classes in San Diego, ISEE Courses & Classes in Seattle, MCAT Courses & Classes in Denver, GMAT Courses & Classes in San Diego, ACT Courses & Classes in Houston, ACT Courses & Classes in Washington DC, MCAT Courses & Classes in Washington DC, MCAT Courses & Classes in Boston, SAT Courses & Classes in Denver, GRE Courses & Classes in Seattle

Popular Test Prep

ISEE Test Prep in New York City, ACT Test Prep in Houston, SSAT Test Prep in Boston, SSAT Test Prep in New York City, ISEE Test Prep in Houston, MCAT Test Prep in Denver, GMAT Test Prep in Miami, SSAT Test Prep in Denver, GMAT Test Prep in Boston, ISEE Test Prep in Miami

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ACT Math : Cubes

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

Example Question #651 : Geometry

Example Question #21 : Cubes

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

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

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

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

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

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

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

All ACT Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: