Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

Create An Account

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #651 : How To Find Rate Of Change

A cube is growing in size. What is the ratio of the rate of growth of the cube's volume to the rate of growth of its sides when its sides have length 110?

Possible Answers:

990 $\displaystyle 990$

1210 $\displaystyle 1210$

12100 $\displaystyle 12100$

36300 $\displaystyle 36300$

108900 $\displaystyle 108900$

Correct answer:

36300 $\displaystyle 36300$

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of the length of its sides:

V=s^3 $\displaystyle V=s^3$

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

$\frac{dV}{dt}=3s^2\frac{ds}{dt}$ $\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}$

Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and sides:

$3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$ $\displaystyle 3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$

$\phi=3s^2$ $\displaystyle \phi=3s^2$

$\phi =3(110)^2=36300$ $\displaystyle \phi =3(110)^2=36300$

Report an Error

Example Question #3571 : Calculus

A cube is growing in size. What is the ratio of the rate of growth of the cube's volume to the rate of growth of its sides when its sides have length 130?

Possible Answers:

1690 $\displaystyle 1690$

16900 $\displaystyle 16900$

1170 $\displaystyle 1170$

50700 $\displaystyle 50700$

5070 $\displaystyle 5070$

Correct answer:

50700 $\displaystyle 50700$

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of the length of its sides:

V=s^3 $\displaystyle V=s^3$

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

$\frac{dV}{dt}=3s^2\frac{ds}{dt}$ $\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}$

Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and sides:

$3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$ $\displaystyle 3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$

$\phi=3s^2$ $\displaystyle \phi=3s^2$

$\phi =3(130)^2=50700$ $\displaystyle \phi =3(130)^2=50700$

Report an Error

Example Question #2541 : Functions

A cube is growing in size. What is the ratio of the rate of growth of the cube's volume to the rate of growth of its sides when its sides have length 47?

Possible Answers:

423 $\displaystyle 423$

6627 $\displaystyle 6627$

141 $\displaystyle 141$

19881 $\displaystyle 19881$

2209 $\displaystyle 2209$

Correct answer:

6627 $\displaystyle 6627$

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of the length of its sides:

V=s^3 $\displaystyle V=s^3$

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

$\frac{dV}{dt}=3s^2\frac{ds}{dt}$ $\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}$

Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and sides:

$3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$ $\displaystyle 3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$

$\phi=3s^2$ $\displaystyle \phi=3s^2$

$\phi =3(47)^2=6627$ $\displaystyle \phi =3(47)^2=6627$

Report an Error

Example Question #3572 : Calculus

A cube is growing in size. What is the ratio of the rate of growth of the cube's volume to the rate of growth of its sides when its sides have length 30?

Possible Answers:

900 $\displaystyle 900$

8100 $\displaystyle 8100$

5400 $\displaystyle 5400$

2700 $\displaystyle 2700$

$\displaystyle 90$

Correct answer:

2700 $\displaystyle 2700$

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of the length of its sides:

V=s^3 $\displaystyle V=s^3$

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

$\frac{dV}{dt}=3s^2\frac{ds}{dt}$ $\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}$

Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and sides:

$3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$ $\displaystyle 3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$

$\phi=3s^2$ $\displaystyle \phi=3s^2$

$\phi =3(30)^2=2700$ $\displaystyle \phi =3(30)^2=2700$

Report an Error

Example Question #751 : Rate

A cube is growing in size. What is the ratio of the rate of growth of the cube's volume to the rate of growth of its sides when its sides have length 32?

Possible Answers:

9216 $\displaystyle 9216$

1024 $\displaystyle 1024$

$\displaystyle 96$

27648 $\displaystyle 27648$

3072 $\displaystyle 3072$

Correct answer:

3072 $\displaystyle 3072$

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of the length of its sides:

V=s^3 $\displaystyle V=s^3$

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

$\frac{dV}{dt}=3s^2\frac{ds}{dt}$ $\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}$

Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and sides:

$3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$ $\displaystyle 3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$

$\phi=3s^2$ $\displaystyle \phi=3s^2$

$\phi =3(32)^2=3072$ $\displaystyle \phi =3(32)^2=3072$

Report an Error

Example Question #752 : Rate

A cube is growing in size. What is the ratio of the rate of growth of the cube's volume to the rate of growth of its sides when its sides have length 95?

Possible Answers:

9025 $\displaystyle 9025$

285 $\displaystyle 285$

855 $\displaystyle 855$

27075 $\displaystyle 27075$

81225 $\displaystyle 81225$

Correct answer:

27075 $\displaystyle 27075$

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of the length of its sides:

V=s^3 $\displaystyle V=s^3$

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

$\frac{dV}{dt}=3s^2\frac{ds}{dt}$ $\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}$

Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and sides:

$3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$ $\displaystyle 3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$

$\phi=3s^2$ $\displaystyle \phi=3s^2$

$\phi =3(95)^2=27075$ $\displaystyle \phi =3(95)^2=27075$

Report an Error

Example Question #2541 : Functions

A cube is diminishing in size. What is the ratio of the rate of loss of the cube's volume to the rate of loss of its sides when its sides have length $\frac{14}{15}$ $\displaystyle \frac{14}{15}$?

Possible Answers:

$\frac{196}{225}$ $\displaystyle \frac{196}{225}$

$\frac{196}{75}$ $\displaystyle \frac{196}{75}$

$\frac{196}{25}$ $\displaystyle \frac{196}{25}$

$\frac{14}{225}$ $\displaystyle \frac{14}{225}$

$\frac{14}{75}$ $\displaystyle \frac{14}{75}$

Correct answer:

$\frac{196}{75}$ $\displaystyle \frac{196}{75}$

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of the length of its sides:

V=s^3 $\displaystyle V=s^3$

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

$\frac{dV}{dt}=3s^2\frac{ds}{dt}$ $\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}$

Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and sides:

$3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$ $\displaystyle 3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$

$\phi=3s^2$ $\displaystyle \phi=3s^2$

$\phi =3(\frac{14}{15})^2=\frac{196}{75}$ $\displaystyle \phi =3(\frac{14}{15})^2=\frac{196}{75}$

Report an Error

Example Question #2541 : Functions

A cube is diminishing in size. What is the ratio of the rate of loss of the cube's volume to the rate of loss of its sides when its sides have length $\frac{13}{9}$ $\displaystyle \frac{13}{9}$?

Possible Answers:

$\frac{169}{81}$ $\displaystyle \frac{169}{81}$

$\frac{169}{9}$ $\displaystyle \frac{169}{9}$

$\frac{13}{81}$ $\displaystyle \frac{13}{81}$

$\frac{13}{27}$ $\displaystyle \frac{13}{27}$

$\frac{169}{27}$ $\displaystyle \frac{169}{27}$

Correct answer:

$\frac{169}{27}$ $\displaystyle \frac{169}{27}$

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of the length of its sides:

V=s^3 $\displaystyle V=s^3$

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

$\frac{dV}{dt}=3s^2\frac{ds}{dt}$ $\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}$

Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and sides:

$3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$ $\displaystyle 3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$

$\phi=3s^2$ $\displaystyle \phi=3s^2$

$\phi =3(\frac{13}{9})^2=\frac{169}{27}$ $\displaystyle \phi =3(\frac{13}{9})^2=\frac{169}{27}$

Report an Error

Example Question #666 : How To Find Rate Of Change

A cube is diminishing in size. What is the ratio of the rate of loss of the cube's volume to the rate of loss of its sides when its sides have length $\frac{11}{4}$ $\displaystyle \frac{11}{4}$?

Possible Answers:

$\frac{363}{16}$ $\displaystyle \frac{363}{16}$

$\frac{363}{4}$ $\displaystyle \frac{363}{4}$

$\frac{121}{4}$ $\displaystyle \frac{121}{4}$

$\frac{121}{8}$ $\displaystyle \frac{121}{8}$

$\frac{121}{16}$ $\displaystyle \frac{121}{16}$

Correct answer:

$\frac{363}{16}$ $\displaystyle \frac{363}{16}$

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its volume in terms of the length of its sides:

V=s^3 $\displaystyle V=s^3$

The rates of change of the volume can be found by taking the derivative of each side of the equation with respect to time:

$\frac{dV}{dt}=3s^2\frac{ds}{dt}$ $\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}$

Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the volume and sides:

$3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$ $\displaystyle 3s^2\frac{ds}{dt}=(\phi)\frac{ds}{dt}$

$\phi=3s^2$ $\displaystyle \phi=3s^2$

$\phi =3(\frac{11}{4})^2=\frac{363}{16}$ $\displaystyle \phi =3(\frac{11}{4})^2=\frac{363}{16}$

Report an Error

Example Question #3575 : Calculus

A cube is growing in size. What is the ratio of the rate of growth of the cube's surface area to the rate of growth of its diagonal when its sides have length $11\sqrt{17}$ $\displaystyle 11\sqrt{17}$?

Possible Answers:

$44\sqrt{51}$ $\displaystyle 44\sqrt{51}$

$132\sqrt{3}$ $\displaystyle 132\sqrt{3}$

$17\sqrt{51}$ $\displaystyle 17\sqrt{51}$

$132\sqrt{17}$ $\displaystyle 132\sqrt{17}$

$33\sqrt{51}$ $\displaystyle 33\sqrt{51}$

Correct answer:

$44\sqrt{51}$ $\displaystyle 44\sqrt{51}$

Explanation:

Begin by writing the equations for a cube's dimensions. Namely its surface area and diagonal in terms of the length of its sides:

A=6s^2 $\displaystyle A=6s^2$

$d=s\sqrt{3}$ $\displaystyle d=s\sqrt{3}$

The rates of change of these can be found by taking the derivative of each side of the equations with respect to time:

$\frac{dA}{dt}=12s\frac{ds}{dt}$ $\displaystyle \frac{dA}{dt}=12s\frac{ds}{dt}$

$\frac{dd}{dt}=\sqrt{3}\frac{ds}{dt}$ $\displaystyle \frac{dd}{dt}=\sqrt{3}\frac{ds}{dt}$

Now, knowing the length of the sides, simply divide to find the ratio between the rate of change of the surface area and diagonal:

$12s\frac{ds}{dt}=(\phi)\sqrt{3}\frac{ds}{dt}$ $\displaystyle 12s\frac{ds}{dt}=(\phi)\sqrt{3}\frac{ds}{dt}$

$\phi=4s\sqrt{3}$ $\displaystyle \phi=4s\sqrt{3}$

$\phi =4(11\sqrt{17})\sqrt{3}=44\sqrt{51}$ $\displaystyle \phi =4(11\sqrt{17})\sqrt{3}=44\sqrt{51}$

Report an Error

View Calculus Tutors

Naomi
Certified Tutor

Earlham College, Bachelor in Arts, Mathematics. Saint Josephs University, Master of Science, Education.

View Calculus Tutors

Deborah
Certified Tutor

Western Michigan University, Master of Science, Mathematics Teacher Education.

View Calculus Tutors

Liliana
Certified Tutor

Georgia Institute of Technology-Main Campus, Bachelor of Engineering, Chemical Engineering.

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Computer Science Tutors in New York City, Biology Tutors in Atlanta, Spanish Tutors in Denver, LSAT Tutors in Dallas Fort Worth, Physics Tutors in Seattle, LSAT Tutors in Philadelphia, Statistics Tutors in San Francisco-Bay Area, Calculus Tutors in Dallas Fort Worth, ACT Tutors in Chicago, Reading Tutors in Boston

Popular Courses & Classes

SSAT Courses & Classes in Philadelphia, SSAT Courses & Classes in Denver, MCAT Courses & Classes in Denver, MCAT Courses & Classes in Los Angeles, LSAT Courses & Classes in New York City, ACT Courses & Classes in Houston, SAT Courses & Classes in Los Angeles, GMAT Courses & Classes in Houston, GMAT Courses & Classes in Phoenix, ISEE Courses & Classes in Chicago

Popular Test Prep

MCAT Test Prep in New York City, ISEE Test Prep in Los Angeles, GRE Test Prep in Los Angeles, SAT Test Prep in Miami, LSAT Test Prep in Chicago, GMAT Test Prep in Washington DC, MCAT Test Prep in Phoenix, ISEE Test Prep in Philadelphia, SAT Test Prep in Los Angeles, LSAT Test Prep in Washington DC

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

Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #651 : How To Find Rate Of Change

Example Question #3571 : Calculus

Example Question #2541 : Functions

Example Question #3572 : Calculus

Example Question #751 : Rate

Example Question #752 : Rate

Example Question #2541 : Functions

Example Question #2541 : Functions

Example Question #666 : How To Find Rate Of Change

Example Question #3575 : Calculus

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: