<p>A cone made of cardboard has a vertical height of 8 cm and a radius of 6 cm. If this cone is cut along the slanted height to make a sector, what is the central angle, in degrees, of the sector?</p>
<p>I can imagine the sector that is made from cutting the cone, but do not know what to do next :(</p>
<p>Answer is the sum of 185+7+11+13 degrees ;)</p>
<p>Well, I am imagining that the whole slant height is cut…</p>
<p>Therefore, I am inagining something like… a sector with radius 10 cm (because, l=sqrt((6^2)+(8^2)))</p>
<p>and the “curve” of the sector, i.e. the length of the “curvy” part would be L= 2(pie)r = 12(pie)</p>
<p>Also, since the radius of the sector is 10 units, we can say that the length of the curvy part is also x times the circumference of te circle with radius 10.</p>
<p>i.e. x<em>2</em>(pie)<em>10=2</em>(pie)*6
=> x = 0.6</p>
<p>Now, 0.6 *360 (degrees) = 216 degrees.
Which is 185+7+11+13</p>
<p>To be honest, I didn’t get this question correct in the first try. After I saw your answer, I tried to think of other ways and voila!</p>
<p>Wow! Thanks for the work-through, now we both know how to approach a problem like this :)</p>