Problem #2058

2058.

Which of the cones listed below can be formed from a $252^\circ$ sector of a circle of radius $10$ by aligning the two straight sides?

[asy] import graph; unitsize(1.5cm); defaultpen(fontsize(8pt));  draw(Arc((0,0),1,-72,180),linewidth(.8pt)); draw(dir(288)--(0,0)--(-1,0),linewidth(.8pt)); label("$10$",(-0.5,0),S); draw(Arc((0,0),0.1,-72,180)); label("$252^{\circ}$",(0.05,0.05),NE); [/asy]

$\text{(A) A cone with slant height of } 10 \text{ and radius } 6$

$\text{(B) A cone with height of } 10 \text{ and radius } 6$

$\text{(C) A cone with slant height of } 10 \text{ and radius } 7$

$\text{(D) A cone with height of } 10 \text{ and radius } 7$

$\text{(E) A cone with slant height of } 10 \text{ and radius } 8$

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Instructions for entering answers:

  • Reduce fractions to lowest terms and enter in the form 7/9.
  • Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
  • Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
  • Exponents should be entered in the form 10^10.
  • If the problem is multiple choice, enter the appropriate (capital) letter.
  • Enter points with parentheses, like so: (4,5)
  • Complex numbers should be entered in rectangular form unless otherwise specified, like so: 3+4i. If there is no real component, enter only the imaginary component (i.e. 2i, NOT 0+2i).

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