Question 771099
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First of all, you didn't specify whether 7 meters was the diameter or the radius of the base.  Given the answers you provided, it had to be the diameter, but in the future, you need to make sure that there are no pieces of given information that you leave out of the problem statement.


Now, your calculations are spot on, but since the answer key is in improper fractions, you should be working in fractions rather than decimals.  For the cylinder part, since the decimal value of the radius squared times the height ended in .5, which is 1/2, you need to multiply by 2 and use 2 as a denominator.  And 73.5 times 2 is indeed 147, so 73.5 is equal to *[tex \LARGE \frac{147}{2}].


The hemisphere part is a little uglier, but if you do the radius cubed computation long hand, you get a clue at an intermediate step.


3.5 times 3.5 is 12.25.  Note that 0.25 is the same as 1/4.  Now, in order to cube the radius you have to multiply 12.25 by 3.5 -- you are putting another factor of 1/2 into the mix, so the final result, 42.875, is the result of multiplying something that has a 1/4 fraction in it times something that has a 1/2 fraction in it, so the .875 must be some number of 8ths.  And if you multiply 42.875 times 8 you get 343 (look a little familiar?), and you can say that 42.875 is equal to *[tex \LARGE \frac{343}{8}].  But wait, you still have to multiply by that pesky *[tex \LARGE \frac{2}{3}] fraction, right?


*[tex \LARGE \frac{343}{8}\ \cdot\ \frac{2}{3}\ =\ \frac{343}{4}\ \cdot\ \frac{1}{3}\ =\ \frac{343}{12}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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