Download POW #2 4 or 24.566 ft of steel band I first constructed a triangle

POW #2
1. 4𝜋 + 12 or 24.566 ft of steel band
2.
a. I first constructed a triangle surrounding the three drums such that each side of
the triangle was tangent to two of the drums within the cluster. In doing this
each drum should have two tangent lines.
b. With the tangent lines, I then created radii from the center of the drums to each
of their tangent lines (two perpendicular segments per drum).
c. I then constructed three segments, parallel to the exterior tangent lines,
connecting the centers of the three circles, forming an equilateral triangle with
side lengths of 4 ft.
d. Looking at the four central angles for each circle, we have two right angles and a
60 degree angle. This makes the fourth angle 120 degrees.(360-(90+90+60)=120)
e. Since a third of the circumference of each drum is wrapped in the steel band, the
amount of steel band in contact with each drum is simply the circumference of a
single drum.
f. This leaves the steel band between each drum which is not in contact. This is
simply the distance between points of tangency. Since I know that the radius of
each drum and I also know that the points of tangency are the distance between
the two centers of corresponding drums, the distance of steel band between
each drum is 4 ft. Multiplying that by three, we have 12 ft of steel band that is
not in contact with the drums.
g. Totaling the length of band in contact and the band not in contact we have 4𝜋 +
12 ft of steel band or 24.566 ft of steel band.
3. Use the techniques established in the problem above to solve a similar problem
including four drums of equal radii.
4. Rules of Tangent Lines:
 When a radius of a circle is drawn to a point of tangency, that radius is
perpendicular to the tangent line containing that point of tangency.
 The sum of the central angles (vertex at center) is 360 degrees.
5. 0014 (Understand properties of points, lines, planes, and space and their relationship to
Euclidean and non-Euclidean geometry.) Demonstrate an understanding of points, lines,
planes, and space and their geometric applications.
6.
a. CCSS.Math.CONTENT.HSG.C.B.5- Derive using similarity the fact that the length
of the arc intercepted by an angle is proportional to the radius, and define the
radian measure of the angle as the constant of proportionality; derive the
formula for the area of a sector.
b. CCSS.MATH.CONTENT.HSG.C.A.4- Construct a tangent line from a point outside a
given circle to the circle.
c. CCSS.MATH.CONTENT.HSG.C.A.2- Identify and describe relationships among
inscribed angles, radii, and chords. Include the relationship between central,
inscribed, and circumscribed angles; inscribed angles on a diameter are right
angles; the radius of a circle is perpendicular to the tangent where the radius
intersects the circle.
7. Your child’s school is planning a silent auction where they will be auctioning off a variety
of different gift baskets. You oversee creating your child’s classroom baskets and are
including 4 identically shaped bottles of different perfumes per basket, in hope to stir
some attention from the mothers, or fathers in search of some brownie points. Each
bottle is 3 inches in diameter, and you wish to wrap them in ribbon for a more pleasant
presentation. If the local craft store sells ribbon for $.05 a yard and you need to create
five baskets, how much would you spend on ribbon? (Allow one inch of overlap for each
segment of ribbon, i.e. five inches in total will be added to your calculated length)