Which of the cones below can be formed froma252◦sector of a circle of radius 10 by aligningthe two straight sides?
(A)
10
6
(B)
10
6
(C)
10
7
(D)
10
7
(E)
10
8
2001 AMC 10, Problem #17
—
2001 AMC 12, Problem #8
—
“The slant height of the cone is 10, the radius of the
sector.”
Solution
Difficulty:
Hard
NCTM
Standard:
Geometry Standard for Grades 9–12:
Analyze properties and determine
attributes of two- and three-dimensional objects.
Mathworld.com Classification:
Geometry
>
Plane Geometry
>
Arcs
>
Circular Sector
Geometry
>
Solid Geometry
>
Cones
The plane is tiled by congruent squares andcongruent pentagons as indicated. The percentof the plane that is enclosed by the pentagonsis closest to
2001 AMC 10, Problem #18—2001 AMC 12, Problem #10—“Draw a3×3pattern.”
9
= 55
5
9
%
0 1 2 3 4 5 6 7 8
0
1
2
3
4
5
6
7
8
9
9
Difficulty:
Medium-hard
NCTM
Standard:
Geometry Standard for Grades 9–12:
Analyze properties and determine
attributes of two- and three-dimensional objects.
Mathworld.com Classification:
Geometry
>
Plane Geometry
>
Polygons
Patwantstobuyfourdonutsfromanamplesupply of three types of donuts:glazed, chocolate,and powdered.How many different selections arepossible?
2001 AMC 10, Problem #19—“Apply Gauss’s Backward Formula (also known as barsand stars).”
Mathworld.com Classification:
Applied Mathematics
>
Numerical Methods
>
Finite Differences
>
Gauss’s Backward Formula
