The surface are of a rectangular prism is 95 square centimeters. What is the surface area of a similar prism with dimensions that are 4 times as great as the original prism?
Accepted Solution
A:
You should have had this answered long before now. Since to get any area of a prism, you must multiply two dimensions together. If they increase by a measure of 4, what happens. I think I'll ignore the 95 for a minute and just make up my own example.
Suppose you have a rectangular prism that measures 2 * 4 * 6. You have 2 faces that are 2*4 which is 8*2 = 16 You have 2 faces that are 2*6 which is 12*2 = 24 You have 2 faces that are 4*6 which is 2*23 = 48 Now the total surface area is 48 + 24 + 16 = 88
Now briefly what happens you you increase each dimension by 4? it becomes 8 * 16 * 24 Two faces with 8 by 16 is 128 * 2 = 256 Two faces with 8 by 24 is 192 * 2 = 384 Two faces with 16 by 24 is 384 * 2 = 768 The total area of this figure is 1408. Just how many times bigger is this than 88. It should be 16 times bigger. Is it?
1408 / 88 = 16. It is.
Now to your question. If the sample is 95 cm^2 then the new prism should be 16 times bigger.