<p>So this is basically the only math problem i couldnt solve and i need some help from you guys ;} It is not the typical kindergarten problems that appear on the SAT .So this is it :</p>
<p>A 5 foot-long cylindrical pipe has an inner diameter of 6 feet and an outer diameter of 8 feet.
If the total surface area is kn(n=Pi) ,what is the value of k ?</p>
<p>(Ugh, I solved this whole thing for volume before I realized it said SA. Fail)</p>
<p>So yea, anywho: the SA of a pipe is the SA of the outer cylinder plus the SA of the small cylinder plus the top and bottom. (Stand the pipe upright to get the visualization.)</p>
<p>The formula for the SA of a cylinder is V = C*h, but we'll replace C with dn just to avoid some steps. So, solve for each SA. (Let SA1 be the larger cylinder and SA2 the smaller).</p>
<p>SA1 = dnh
=(8)(5)n
=40n</p>
<p>SA2 = dnh
= (6)(5)n
=30n</p>
<p>So now we need to find the top and bottom. The top and bottom follow the same idea. To find the top (which is equal to the bottom), you need to subtract the area of the inner "circle" from the area of what the top would be if the pipe were just a cylinder. Hard to explain, so I'll just do it out.</p>
<p>The area of the top of a cylinder is just a circle. Set up that equation, using 4 for the radius, since we're dealing with the "larger circle."
A1 = nr^2
=16n</p>
<p>Now, subtract the area of the "smaller circle" (or lack thereof, if you will). Use 3 as the radius, since its d is given as 6.</p>
<p>A2 = nr^2
=9n</p>
<p>Subtract the two (A1 - A2 = overall A of the top):
16n - 9n = 7n</p>
<p>The bottom is the same, so add another 7n:
7n + 7n = 14n</p>
<p>Add all the parts up:
14n + 30n + 40n = 84n.</p>
<p>Since kn = total SA = 84n, k =84.</p>
<p>This doesn't seem like a real SAT problem, simply because it takes too long to solve. A real SAT problem would only ask for one piece, but maybe disguise it better. Where did you find this one?</p>
<p>I got k= 84 too, so check. I am too lazy to type it all up. You can see the method from Godfatherbob^
It wasn't a hard problem at all. Took me probably a minute...</p>
<p>this doesnt look like a sat question.</p>
<p>No it isnt a hard problem, but it requires a little bit of more calculation than usual. Id say questions like this are likely to appear at the very end of sections, to freak you when you are running out of time.</p>
<p>84 is the answer and the problem is from Barron`s how to prepare for the SAT.It is in the Solid geometry section.</p>
<p>A 5 foot-long cylindrical pipe has an inner diameter of 6 feet and an outer diameter of 8 feet.
If the total surface area is kn(n=Pi) ,what is the value of k ?</p>
<p>Area = 2.pi.r.h + 2.pi.R. h + 2[ pi(R^2 - r^2)]
= 2.pi.5 (3 + 4) + 2[pi (4^2 - 3^2)]
= pi.70 + 2.pi.7
= 84.pi
so k = 84</p>
<p>Yes, I solved this problem in the same way as Spideyunlimited and it took practically one minute! The words are all straightforward and the concepts are familiar</p>
<p>k = 84…</p>
<p>did that **** in my head…took two minutes…</p>
<p>it is rather kindergarten lol</p>