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Calculus 1 : Rate of Change

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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 volume if its sides have a length of 7 and a rate of growth of 34?

Possible Answers:

238

169932

4998

1666

714

Correct answer:

4998

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 7 and a rate of growth of 34

$\frac{dV}{dt}=3(7)^2(34)=4998$

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Example Question #782 : 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 8 and a rate of growth of 33?

Possible Answers:

6336

192

704

2112

Correct answer:

6336

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 8 and a rate of growth of 33:

$\frac{dV}{dt}=3(8)^2(33)=6336$

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Example Question #783 : 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 9 and a rate of growth of 32?

Possible Answers:

7776

2592

82944

248832

864

Correct answer:

7776

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 9 and a rate of growth of 32:

$\frac{dV}{dt}=3(9)^2(32)=7776$

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Example Question #784 : 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 10 and a rate of growth of 31?

Possible Answers:

930

3100

9300

310

96100

Correct answer:

9300

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 10 and a rate of growth of 31:

$\frac{dV}{dt}=3(10)^2(31)=9300$

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Example Question #785 : 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 11 and a rate of growth of 30?

Possible Answers:

108900

990

10890

3630

330

Correct answer:

10890

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 11 and a rate of growth of 30:

$\frac{dV}{dt}=3(11)^2(30)=10890$

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Example Question #786 : 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 12 and a rate of growth of 29?

Possible Answers:

348

121104

4176

1044

12528

Correct answer:

12528

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 12 and a rate of growth of 29:

$\frac{dV}{dt}=3(12)^2(29)=12528$

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Example Question #787 : 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 12 and a rate of growth of 29?

Possible Answers:

12528

25056

4176

1392

348

Correct answer:

4176

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 12 and a rate of growth of 29:

$\frac{dA}{dt}=12(12)(29)=4176$

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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:

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

Report an Error

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:

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

Report an Error

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:

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

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 #781 : How To Find Rate Of Change

Example Question #782 : How To Find Rate Of Change

Example Question #783 : How To Find Rate Of Change

Example Question #784 : How To Find Rate Of Change

Example Question #785 : How To Find Rate Of Change

Example Question #786 : How To Find Rate Of Change

Example Question #787 : How To Find Rate Of Change

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

All Calculus 1 Resources

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