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/
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