volumes

course Mth 271

002. Volumes

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Question: `q001. What is the volume of a rectangular solid whose dimensions are exactly 3 cm by 5 cm by 7 cm?

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Your solution:

V = ah

V = (5)(7)

V = 35

Confidence Assessment:

OK

Self-critique Rating:

To find the solution, I used the equation for volume of a rectangle

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Question: `q002. What is the volume of a rectangular solid whose base area is 48 square meters and whose altitude is 2 meters?

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Your solution:

v = ah

v = (48)(2)

v = 96

Confidence Assessment:

OK

Self-critique Rating:

To find the solution, I used the rectangle volume equation.

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Question: `q003. What is the volume of a uniform cylinder whose base area is 20 square meters and whose altitude is 40 meters?

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Your solution:

V = ah

V = (20)(40)

V = 800

Confidence Assessment:

OK

Self-critique Rating:

To find the solution, I used the volume equation for uniform cylinders.

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Question: `q004. What is the volume of a uniform cylinder whose base has radius 5 cm and whose altitude is 30 cm?

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Your solution:

V = ah

A = pi( r)^2

A = pi(5)^2

A = pi(25)

A = 78.54

V = (78.54)(30)

V = 2356.2

Confidence Assessment:

OK

Self-critique Rating:

To find the volume, I had to use the values given (radius and height) to find the area of the circle and then the volume.

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Question: `q005. Estimate the dimensions of a metal can containing food. What is its volume, as indicated by your estimates?

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Your solution:

Different cans have different volumes.

Confidence Assessment:

OK

Self-critique Rating:

Because no dimensions were given, the volume of a can containing cannot be estimated.

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Question: `q006. What is the volume of a pyramid whose base area is 50 square cm and whose altitude is 60 cm?

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Your solution:

V = 1/3ah

V = 1/3(50)(60)

V = 1000

Confidence Assessment:

OK

Self-critique Rating:

To find the volume, I used the equation for the volume of a pyramid

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Question: `q007. What is the volume of a cone whose base area is 20 square meters and whose altitude is 9 meters?

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Your solution:

V = 1/3ah

V = 1/3(2)(9)

V = 6

Confidence Assessment:

OK

Self-critique Rating:

To find the volume, I used the volume equation for a cone.

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Question: `q008. What is a volume of a sphere whose radius is 4 meters?

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Your solution:

V = 4/3pi( r)^3

V = 4/3pi(4)^3

V = 4/3pi(64)

V = 268.08

Confidence Assessment:

OK

Self-critique Rating:

To find the volume, I used the volume equation for the sphere

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Question: `q009. What is the volume of a planet whose diameter is 14,000 km?

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Your solution:

D = 1/2r

(14000) = ½r

D = 700

V = 4/3pi( r)^3

V = 4/3pi( 7000)^3

V = 14.3*10^11

Confidence Assessment:

OK

Self-critique Rating:

To find the volume of this sphere, I first had to use the diameter equation to find the radius

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Question: `q010. Summary Question 1: What basic principle do we apply to find the volume of a uniform cylinder of known dimensions?

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Your solution:

The basic principle is that the cylinder is uniform, meaning the dimensions are constant.

Confidence Assessment:

OK

Self-critique Rating:

This is a logic problem.

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Question: `q011. Summary Question 2: What basic principle do we apply to find the volume of a pyramid or a cone?

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Your solution:

The volume of these shapes is equal to 1/3 of its base multiplied by its height

Confidence Assessment:

OK

Self-critique Rating:

This is a logic question.

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Question: `q012. Summary Question 3: What is the formula for the volume of a sphere?

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Your solution:

V = 4/3pi( r)^3

Confidence Assessment:

OK

Self-critique Rating:

I wrote down the equation for the volume of a sphere.

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Question: `q013. Explain how you have organized your knowledge of the principles illustrated by the exercises in this assignment.

Self-critique Rating:

This exercise served as a refresher course for volumes.

&#Very good work. Let me know if you have questions. &#