<p>A spherical ball of clay w/ a radius of 2 in. contains exactly enough clay to make a brick. How many such bricks could be made using the amount of clay in a spherical ball with a radius of 4 in.? (V=4/3pir^3)</p>
<p>answer is 16</p>
<p>If a/b=1/k, which of the following must be equal to 1?
a) a
b) k
c) bk
d) b/a
e) ak/b</p>
<p>answer is e (why not a, isn't a=1)</p>
<p>Problem 1:</p>
<p>Find the ratio of the volume of the second sphere to the volume of the first sphere. This will tell you how many times bigger (in volume) the second sphere is, and how many times more bricks it can produce.</p>
<p>(V<em>2) / (V</em>1) = [(4/3) * pi * ((r<em>2)^3)] / [(4/3) * pi * ((r</em>1)^3)] </p>
<p>The 4/3's and pi's cancel, leaving us with</p>
<p>(V<em>2) / (V</em>1) = ((r<em>2)^3) / ((r</em>1)^3)</p>
<p>Plug in your numbers.</p>
<p>(V<em>2) / (V</em>1) = ((4 in)^3) / ((2 in)^3)</p>
<p>(V<em>2) / (V</em>1) = (64 (in^3)) / (8 (in^3))</p>
<p>The inches cubed cancel, leaving the ratio as:</p>
<p>(V<em>2) / (V</em>1) = 64 / 8</p>
<p>(V<em>2) / (V</em>1) = 8</p>
<p>So sphere 2 is 8 times as big as sphere 1, and therefore can make 8 times as many bricks (8 x 1 = 8).</p>
<p>...are you SURE the answer is 16? You didn't copy anything wrong?</p>
<p>Problem 2:</p>
<p>Let us solve for 1 by multiplying both sides by k.</p>
<p>(ak/b) = 1.</p>
<p>Clearly, e is the answer. All the other ones CAN be 1, but there is no guarantee.</p>
<p>A isn't equal to 1. (a/b) = (1/k) does not imply a = 1 or b = k. For the sake of counterexample, let us consider:</p>
<p>(2/1) = (4/2)</p>
<p>Although the statement is corrent, 2 =/= 4 and 1 =/= 2. Same idea.</p>
<p>For the first one I got an 8 too.
You simply divide the volume of the larger ball by the volume of the smaller ball. Doing so, u get an 8.</p>
<p>about example 2 ,a ,b and k can be 1 but you must find which MUST be 1</p>
<p>Block of clay problem: </p>
<p>V = 4/3pi(r^3) = 4/3(pi)(8) = 32/3pi
V2 = 4/3pi(64)
= 256/3pi </p>
<p>256/32 = ** 8 **</p>