Download Accel Geo Ch 7 Review - SOLUTIONS

Geometry
Name______________________
Review HW for Unit Quiz: Areas & Volumes
Directions: Please answer all questions and show work on the problems that merit discussion and require that
an argument be made. Calculators are allowed. Leave ALL answers in exact form (in terms of  , for example)
if possible. When reporting approximate answers, round to the nearest 0.001 (thousandth).
1. After school one day, Ms. Knaus and Mr. Platt decide to stop grading and build a rocket,
only using shapes studied recently in Geometry class. They decide to take a cylinder with
a height of 40 inches and a radius of 6 inches and add to it a conical tip with a height of 8
inches. The bottom of the rocket is a hemisphere glued on to the base of the cylinder. Find
the total exposed surface area of the rocket.
2. Find the ratio of area (I) to area (II).
Geometry
3. Consider an unfolded cone (the “PacMan” shape we have worked with).
radius (of cone base)


Using this shape, show that
.
slant height
360

4. Find the area of the shaded region, given that each segment length in this cross is 4 cm (you
may assume that the segments meet at right angles).
5.
Geometry
Consider a right circular cylindrical cake with a volume of 72 cubic inches and a height
of 8 inches. You cut a slice that represents 1/6 of the total cake and remove this slice.
Calculate the following:
a. the radius of the cake
b. the total surface area of the slice you remove from the cake (a model of this yummy
slice is provided below).
Geometry
6. The shorter diagonal of a parallelogram has a length of 10 cm and it divides the opposite
angles of the parallelogram into angles of 40 degrees and 80 degrees. Find:
7.
a.
the area of the parallelogram.
b.
the dimensions (length & height) of the parallelogram.
Geometry
An octahedron (which can be seen as two regular square pyramids attached at the bases
such that every edge of the figure is congruent) is shown below. If one of the edges is of
length 2, answer the following:
a.
b.
Determine the volume of the octahedron
If this octahedron fits perfectly inside of a cylindrical container, what percentage of
the container would be filled by the octahedron?
Geometry
8. This question requires that a thought-process be clearly expressed in words, in addition to
the mathematical analysis. The diagram is of a regular polygon inscribed in a circle.
a. Using the diagram as an aid, present an argument that the area for a n-sided regular
polygon is given by the following:
AREG POLYGON 
1
 a  p  , where
2
a is the distance from the center of a polygon to any
one side of the regular polygon and
p is the perimeter of the regular polygon.
a
s
b. Suppose you are to keep this same circle, but let the number of sides increase
without bound. Clearly explain how each part of the above formula would change
so as to arrive at the formula for a regular polygon with an infinite number of sides
inscribed in a circle.