Volume of Cube, Tent

Date: 7/9/96 at 0:25:2
From: Anonymous
Subject: Volume of Cube, Tent

I have been asked to calculate the volume of several objects.  I was 
able to do one, calculating the volume of a cylinder. But I am not 
sure how to calculate the last three.

They are:

1) a square 3cm x 3cm x 3cm (L x W x H)
2) a rectangle 5cm x 2cm x 4cm (L x W x H)
3) a tent: length = 8cm  the base is 4cm and the slope is 6cm
 
                                ^ 
                               /|\
                              / | \6cm
                             /__|__\ 
                               4cm      

And to top it off, I'm suppose to calculate the capacity of the 
cylinder and the tent.

Can you help?  Is there a basic formula?

Thanks.

Date: 7/14/96 at 21:58:9
From: Doctor Jerry
Subject: Re: Volume of Cube, Tent

I'll start with your last question (Is there a basic formula?).  One 
of the things that calculus offers is a method to calculate the 
volumes of many kinds of figures.  Not a single formula, but a single 
method.  However, since I don't know if you have completed a calculus 
course my answer is that, no, there is no single formula for volume 
that includes many different shapes.

Next, your question 1).  You say "square" but I think you must mean 
cube. The formula for the volume of a rectangular parallelepiped (a 
box) of length L, width W, and height H is V=L*W*H. So, the volume of 
the cube is V=3*3*3=27 cm^3.

The volume of the rectangle (box) is V=5*2*4=40 cm^3.

Finally, the volume of the tent is the area of the triangle times the 
length of the tent.  If by slope you mean that the length of the 
slanted side of the tent is 6 cm, then the height of the triangular 
cross-section of the tent is sqrt(36-4)=sqrt(32).  So, V=(1/2)*base*
height*length=(1/2)*2*sqrt(32)*8=8sqrt(32) cm^3.

I hope I've understood your questions.

-Doctor Jerry,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/