document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210141>Question 1210141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a cross section of a sphere is 64\% of the largest possible cross sectional area of the sphere. If the sphere has radius 1/2, what is the area of the cross section?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851363 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851363\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the sphere have radius $r$.<BR>\n" );
document.write( "The largest possible cross-sectional area of the sphere is a circle with radius $r$, so its area is $\pi r^2$.<BR>\n" );
document.write( "Given that the radius of the sphere is $r = \frac{1}{2}$, the largest possible cross-sectional area is $\pi (\frac{1}{2})^2 = \frac{\pi}{4}$.\r<BR>\n" );
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document.write( "The area of the cross section is 64\% of the largest possible cross-sectional area.<BR>\n" );
document.write( "Therefore, the area of the cross section is $0.64 \cdot \frac{\pi}{4}$.<BR>\n" );
document.write( "$$ 0.64 \cdot \frac{\pi}{4} = \frac{64}{100} \cdot \frac{\pi}{4} = \frac{16}{25} \cdot \frac{\pi}{4} = \frac{4\pi}{25} $$\r<BR>\n" );
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document.write( "Thus, the area of the cross section is $\frac{4\pi}{25}$.\r<BR>\n" );
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document.write( "Final Answer: The final answer is $\boxed{\frac{4 \pi}{25}}$<BR>\n" );
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