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Calculus 1 : Rate of Change

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Example Questions

Example Question #771 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of one of the cube's faces if its sides have a length of 4 and a rate of growth of 10?

Possible Answers:

800

320

3200

Correct answer:

Explanation:

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

a=s^2

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

$\frac{da}{dt}=2s\frac{ds}{dt}$

Once we have the rate equation for the area of the face, we can use what we know about the cube, specifically that its sides have a length of 4 and a rate of growth of 10:

$\frac{da}{dt}=2(4)(10)=80$

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Example Question #772 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of one of the cube's faces if its sides have a length of 22 and a rate of growth of 2?

Possible Answers:

968

528

1936

Correct answer:

Explanation:

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

a=s^2

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

$\frac{da}{dt}=2s\frac{ds}{dt}$

Once we have the rate equation for the area of the face, we can use what we know about the cube, specifically that its sides have a length of 22 and a rate of growth of 2

$\frac{da}{dt}=2(22)(2)=88$

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Example Question #773 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of one of the cube's faces if its sides have a length of 2 and a rate of growth of 23?

Possible Answers:

552

529

2116

1104

Correct answer:

Explanation:

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

a=s^2

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

$\frac{da}{dt}=2s\frac{ds}{dt}$

Once we have the rate equation for the area of the face, we can use what we know about the cube, specifically that its sides have a length of 2 and a rate of growth of 23:

$\frac{da}{dt}=2(2)(23)=92$

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Example Question #774 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of one of the cube's faces if its sides have a length of 3 and a rate of growth of 25?

Possible Answers:

3750

150

1875

900

450

Correct answer:

150

Explanation:

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

a=s^2

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

$\frac{da}{dt}=2s\frac{ds}{dt}$

Once we have the rate equation for the area of the face, we can use what we know about the cube, specifically that its sides have a length of 3 and a rate of growth of 25:

$\frac{da}{dt}=2(3)(25)=150$

Report an Error

Example Question #775 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 1 and a rate of growth of 40?

Possible Answers:

120

1600

2400

4800

Correct answer:

120

Explanation:

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

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:

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

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 1 and a rate of growth of 40:

$\frac{dV}{dt}=3(1)^2(40)=120$

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Example Question #776 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 2 and a rate of growth of 39?

Possible Answers:

234

156

468

Correct answer:

468

Explanation:

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

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:

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

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 2 and a rate of growth of 39:

$\frac{dV}{dt}=3(2)^2(39)=468$

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Example Question #777 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 3 and a rate of growth of 38?

Possible Answers:

114

171

342

1026

Correct answer:

1026

Explanation:

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

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:

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

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 3 and a rate of growth of 38:

$\frac{dV}{dt}=3(3)^2(38)=1026$

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Example Question #778 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 4 and a rate of growth of 37?

Possible Answers:

4736

2368

296

1776

592

Correct answer:

1776

Explanation:

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

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:

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

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 4 and a rate of growth of 37:

$\frac{dV}{dt}=3(4)^2(37)=1776$

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Example Question #779 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 5 and a rate of growth of 36?

Possible Answers:

900

540

180

8100

2700

Correct answer:

2700

Explanation:

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

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:

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

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 5 and a rate of growth of 36:

$\frac{dV}{dt}=3(5)^2(36)=2700$

Report an Error

Example Question #780 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's volume if its sides have a length of 6 and a rate of growth of 35?

Possible Answers:

3780

1260

630

210

7560

Correct answer:

3780

Explanation:

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

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:

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

Now with this known, we can solve for the rate of change of the volume of the cube knowing the condition of cube, in particular that its sides have a length of 6 and a rate of growth of 35:

$\frac{dV}{dt}=3(6)^2(35)=3780$

Report an Error

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Calculus 1 : Rate of Change

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #771 : How To Find Rate Of Change

Example Question #772 : How To Find Rate Of Change

Example Question #773 : How To Find Rate Of Change

Example Question #774 : How To Find Rate Of Change

Example Question #775 : How To Find Rate Of Change

Example Question #776 : How To Find Rate Of Change

Example Question #777 : How To Find Rate Of Change

Example Question #778 : How To Find Rate Of Change

Example Question #779 : How To Find Rate Of Change

Example Question #780 : How To Find Rate Of Change

All Calculus 1 Resources

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