Math Is Fun Forum

basketballstar123

Member

Registered: 2016-08-10

Posts: 11

Geometry

Problem 1:  Let $ABCDEFGH$ be a rectangular prism, as shown, where $AB = 2$, $AD = 3$, and $AE = 5$. Find the volume of pyramid $ACFH$.

Last edited by basketballstar123 (2016-09-07 08:04:46)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry

I have the posters word that he is not affiliated with compuhigh, so this thread is opened for business.

You might want to look here...

http://www.mathisfunforum.com/viewtopic.php?id=20525

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry

The base area AFH and height from C may be difficult to calculate but there is a remedy. One can take projection of AFH on any convenient plane say FEH.This area multiplied by 1/3 times height along a slant line perpendicular to FEH till it meets AEH. This looks uncertain but we can imagine another like  prism flush with surface EFGH its farthest face being E'F'G'H'. One can see that FG'H is a continuation of the plane AFH and CG' is the slant height from C to the base AFH. Area FEH=1/2*FE*EH=1/2*2*3 =3 sq.units. CG'=2*5=10 So the volume of pyramid= 1/3*3*10=10 cubic units.

Inadverdently  AFH was referred to as AEH. Now it stands corrected.

Last edited by thickhead (2016-09-08 05:04:50)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
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thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry

If the above concept is non palatable one can subtract the volume of 4 pyramids ACDH,ACFB,GCFH and EAFH from the volume of prism.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

basketballstar123

Member

Registered: 2016-08-10

Posts: 11

Re: Geometry

Thank you!!!  I got it.  Next Prob:

In right triangle $ABC$ with $\angle B = 90^\circ$, we have $\sin A = 2\cos A$. What is $\cos A$?

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry

Please let me know whether you have accepted #3 or #4.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

basketballstar123

Member

Registered: 2016-08-10

Posts: 11

Re: Geometry

^Those were correct.  Thanks!!   Do you have any ideas for other prob I posted?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Geometry

hi basketballstar123

In right triangle $ABC$ with $\angle B = 90^\circ$, we have $\sin A = 2\cos A$. What is $\cos A$?

Divide the equation by cosA and you'll have a value for tanA.  Make a right angled triangle with opposite and adjacent known and work out the hypotenuse.

Bob

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Children are not defined by school ...........The Fonz
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Sometimes I deliberately make mistakes, just to test you!  …………….Bob

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}