Find the volume of the solid who cross-sections room equilateral triangles and whose basic is a decaying of radius

You are watching: Is it possible to create an equilateral triangle cross section



Correct answer:
Explanation:
Because the disc is that radius R, the base is identified by the adhering to formula:

The correct formula for the area of an it is provided triangle is as follows:


By applying this formula to our general volume formula


The radius R specifies the bounds as being



Putting it all together, the following is obtained:

*Note: the problem did no specify if the overcome sections were perpendicular to the




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Example inquiry #2 : uncover Cross Sections: triangle & Semicircles
Find the volume that the solid whose base is bounded through the one


Possible Answers:
Correct answer:

Explanation:
Because the base is a one of radius


The area of a appropriate isosceles triangle have the right to be uncovered using the formula




The expression because that




Putting it every together, the adhering to is obtained:


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Example question #3 : uncover Cross Sections: triangles & Semicircles
Identify the correct expression for the volume of the solid who cross-sections space equilateral triangle perpendicular come the



Possible Answers:
Correct answer:

Explanation:
First, the cross sections being perpendicular to the


The area the an it is intended triangle is




The intersection clues of the functions






The base is bounded by








Putting it all together, the complying with is obtained:

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Example inquiry #4 : discover Cross Sections: triangles & Semicircles
Identify the correct expression because that the volume of the hard whose basic is bounded by




Possible Answers:
Correct answer:

Explanation:
First, the cross sections being perpendicular come the






The intersection point out of the functions defining the an ar are




The basic is bounded through





Putting it every together, the adhering to is obtained:

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Example inquiry #5 : uncover Cross Sections: triangle & Semicircles
Find the volume that the solid who cross-sections are equilateral triangles and also whose base is a decaying of radius

Possible Answers:
Correct answer:

Explanation:
Because the disc is the radius


The exactly formula for the area of an it is intended triangle is together follows:

By applying this formula to our general volume formula


The radius





Putting it all together, the complying with is obtained:


*Note: the difficulty did not specify if the overcome sections to be perpendicular come the




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Example concern #6 : uncover Cross Sections: triangles & Semicircles
Find the expression because that the volume the the solid who cross-sections are semicircles perpendicular to the



Possible Answers:
Correct answer:

Explanation:
Since the cross-sections space perpendicular come the


The area the a semicircle is



Since the region bounded through






Next, one expression for






Putting this every together, we find the following:

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Example inquiry #7 : find Cross Sections: triangles & Semicircles
Find the volume that the solid who cross-sections space semicircles and also whose base is bounded through the circle

Possible Answers:
Correct answer:

Explanation:
The base is characterized by the complying with formula:




The exactly formula for the area the a semicircle is as follows:

By using this formula to our basic volume formula


Next, one expression for





Putting this every together, we uncover the following:


*Note: the trouble did no specify if the cross sections were perpendicular to the




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Example concern #8 : find Cross Sections: triangle & Semicircles
Identify the exactly expression because that the volume that the solid whose cross-sections space semicircles perpendicular to the



Possible Answers:
Correct answer:

Explanation:
Since the cross-sections room perpendicular come the


The area that a semicircle is



Since the an ar bounded by






Next, an expression for





Putting this every together, we find the following:

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Example concern #9 : discover Cross Sections: triangles & Semicircles
Identify the correct expression because that the volume of the solid whose cross-sections are semicircles perpendicular to the



Possible Answers:
Correct answer:

Explanation:
Since the cross-sections are perpendicular come the


The area the a semicircle is



Since the region bounded by






Next, an expression for






Putting this every together, we discover the following:

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Example question #10 : find Cross Sections: triangle & Semicircles
Identify the exactly expression because that the volume of the solid whose cross-sections space semicircles parallel come the y axis and whose base is bounded through



Possible Answers:
Correct answer:

Explanation:
The cross-sections space parallel come the



The area the a semicircle is



Since the region is bounded by








See more: Thread: How Many Btus Does A Human Body Produce ? Was Morpheus Right
Next, an expression for





Putting this all together, we uncover the following:

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