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Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

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

Example Questions

Example Question #781 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 11 and a rate of growth of 30?

Possible Answers:

220

660

3960

3630

330

Correct answer:

3960

Explanation:

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

A=6s^2

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

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

Now, with the rate equation known, we can solve for the rate of change of the surface area with what we know about the cube, namely that its sides have a length of 11 and a rate of growth of 30:

$\frac{dA}{dt}=12(11)(30)=3960$

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Example Question #789 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 10 and a rate of growth of 31?

Possible Answers:

576600

96100

1860

18600

3720

Correct answer:

3720

Explanation:

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

A=6s^2

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

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

Now, with the rate equation known, we can solve for the rate of change of the surface area with what we know about the cube, namely that its sides have a length of 10 and a rate of growth of 31:

$\frac{dA}{dt}=12(10)(31)=3720$

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Example Question #790 : How To Find Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 9 and a rate of growth of 32?

Possible Answers:

3456

1728

576

2304

6912

Correct answer:

3456

Explanation:

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

A=6s^2

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

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

Now, with the rate equation known, we can solve for the rate of change of the surface area with what we know about the cube, namely that its sides have a length of 9 and a rate of growth of 32:

$\frac{dA}{dt}=12(9)(32)=3456$

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Example Question #871 : Rate

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 8 and a rate of growth of 33?

Possible Answers:

1264

528

2112

69696

3168

Correct answer:

3168

Explanation:

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

A=6s^2

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

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

Now, with the rate equation known, we can solve for the rate of change of the surface area with what we know about the cube, namely that its sides have a length of 8 and a rate of growth of 33:

$\frac{dA}{dt}=12(8)(33)=3168$

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Example Question #792 : Rate Of Change

A cube is growing in size. What is the rate of growth of the cube's surface area if its sides have a length of 7 and a rate of growth of 34?

Possible Answers:

2856

679728

56644

97104

1666

Correct answer:

2856

Explanation:

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

A=6s^2

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

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

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 7 and a rate of growth of 34:

$\frac{dA}{dt}=12(7)(34)=2856$

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Example Question #793 : Rate Of Change

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

Possible Answers:

22050

1260

44100

7350

2520

Correct answer:

2520

Explanation:

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

A=6s^2

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

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

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 6 and a rate of growth of 35:

$\frac{dA}{dt}=12(6)(35)=2520$

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Example Question #794 : Rate Of Change

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

Possible Answers:

10800

5400

2160

180

900

Correct answer:

2160

Explanation:

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

A=6s^2

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

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

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 5 and a rate of growth of 36:

$\frac{dA}{dt}=12(5)(36)=2160$

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Example Question #795 : Rate Of Change

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

Possible Answers:

14208

592

296

1184

1776

Correct answer:

1776

Explanation:

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

A=6s^2

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

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

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 4 and a rate of growth of 37:

$\frac{dA}{dt}=12(4)(37)=1776$

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Example Question #796 : Rate Of Change

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

Possible Answers:

684

1368

4104

342

2052

Correct answer:

1368

Explanation:

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

A=6s^2

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

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

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 3 and a rate of growth of 38:

$\frac{dA}{dt}=12(3)(38)=1368$

Report an Error

Example Question #797 : Rate Of Change

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

Possible Answers:

936

312

Correct answer:

936

Explanation:

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

A=6s^2

The rate of change of the surface area can be found by taking the derivative of each side of the equation with respect to time:

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

Now that we have a relationship between the surface area and the side parameters, we can use what we were told about the cube, in particular that its sides have a length of 2 and a rate of growth of 39:

$\frac{dA}{dt}=12(2)(39)=936$

Report an Error

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Calculus 1 : Calculus

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #781 : How To Find Rate Of Change

Example Question #789 : How To Find Rate Of Change

Example Question #790 : How To Find Rate Of Change

Example Question #871 : Rate

Example Question #792 : Rate Of Change

Example Question #793 : Rate Of Change

Example Question #794 : Rate Of Change

Example Question #795 : Rate Of Change

Example Question #796 : Rate Of Change

Example Question #797 : Rate Of Change

All Calculus 1 Resources

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