Same Surface Area and Volume
Date: 03/28/2001 at 11:21:17 From: Zansia Solis Subject: Surface Area and Volume How can I find two rectangular prisms with the same surface area but different volumes? Also how can I find two cylinders with the same surface area and different volumes?
Date: 03/28/2001 at 12:48:17 From: Doctor Peterson Subject: Re: Surface Area and Volume Hi, Zansia. I would do the same thing in both cases. First choose the dimensions for one of the two objects, and find its area and volume. Now change the base; in the first case, perhaps divide the length by 2. Take the height as an unknown, and write an equation that says the surface area of the new shape is the number you got for the first shape. Solve this for h, and you will have a shape with the same surface area; check its volume to make sure it is different. Here's an example: for an l x w x h rectangular prism, S = 2(lw + lh + wh) V = lwh If I choose l = 4 cm, w = 3 cm, and h = 2 cm, I get S = 2(4*4 + 4*2 + 3*2) = 2(16+8+6) = 60 cm^2 V = 4*3*2 = 24 cm^3 Now for my second cube, I will change l to 2 cm, keep w the same, and leave h unknown. Now S = 2(2*3 + 2h + 3h) V = 2*3*h You want to solve the equation 2(2*3 + 2h + 3h) = 60 and then check that 2*3*h is not 24. If you don't know the formulas you need, click on "Formulas" in our FAQ. http://mathforum.org/dr.math/faq/formulas/ - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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