Chapter 1: Polynomial Functions
Sample Solution—Homemade Waffle Cones
a.
What is the slant height of the cone? Did you need to use a ruler to
determine this measurement? Explain.
The slant height of the cone is the radius of the circle it was constructed from,
so the slant height is approximately 10.5 centimeters.
b. Without measuring, write an equation for the radius of the base of the cone
you constructed in terms of the arc length you removed from the circle.
[Hint: Write an equation for the circumference of the base of the cone first.]
The circumference of the base of the cone is the circumference of the paper
circle less the arc length removed. Since the diameter of the paper circle is 21
centimeters, the circumference is 21
S
centimeters. Therefore, the
circumference of the base of the cone is 21
S
centimeters less the length of the
arc removed, a, or 21
S
a centimeters.
To find the radius of the base of the cone, we recall the formula for the
circumference of a circle is C = 2
S
r. Solving this equation for the radius, r,
gives the circumference divided by 2
S
. So, the radius of the base of the cone
is r =
S
S
2
21 a
= 10.5
S
2
a
.
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