Download Homework 7 Solutions

(2) (2) The answer is correct so the student gets 10 points
(3) The picture for the side is correct, but the picture for the front needs the
top square to be shifted one unit to the left, and the picture for the left
needs the top square to be shifted one unit to the right. I would give the
student 3 points
(5) The picture for the top and the front is correct, but the picture for the
side has an extra square on the right of the bottom row that doesn’t
belong there. I would give them 7 points.
(6) The answer is correct so the student gets 10 points
(3) (a) All of the faces are polygons, so this solid is a polyhedron
(b) One of the faces is a circle, which is not a polygon, so the solid is not a
polyhedron.
(c) One of the faces is a semicircle, which is not a polygon, so the solid is
not a polyhedron
(d) All of the faces are polygons, so this solid is a polyhedron
(5) (a) The solid is neither a pyramid nor a prism since it isn’t a polyhedron.
The circle faces aren’t polygons
(b) The solid is a pyramid because there is only one base and the latral faces
are triangles.
(c) The solid is a prism because there are two congruent parallel bases and
the lateral faces are parallelograms.
(d) The solid is neither a pyramid nor a prism because there is only one
base like a pyramid, but unlike the pyramid, the lateral faces are not all
triangles.
(7) (a) The base of the pyramid is a hexagon, so the figure is a hexagonal pyramid
(b) The bases of the prism are pentagons, so the figure is a pentagonal prism
(18) (a) The statement is false. A triangular prism has two triangular faces and
3 parallelogram faces.
(b) The statement is true. An octahedron is made by joining the bases of 2
square pyramids together.
(c) The statement is false. The net of a dodecahedron is made up of pentagons and pentagons can’t be tessellated.
(d) The statement is true. A tetrahedron has 6 congruent edges.
(20) The skateboard ramp has 2 parallel triangle faces as bases and the lateral
faces are parallelograms, so it resembles a triangular prism. It has 5 faces, 6
vertices and 9 edges.
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(24) The rectangular pyramid and the triangular pyramid are both polyhedra that
have a single base and whose lateral sides are parallelograms. The difference
between them is that the rectangular pyramid has a rectangle for the base,
and the triangular pyramid has a triangle for the base.
(26) The student misremembered Euler’s formula. It should be F + V = E + 2.
Since there are 6 faces and 10 edges, 6 + V = 10 + 2, So 6 + V = 12. Hence
V = 6. I would encourage the student to review the section on Euler’s formula.
(30) (a) 2 other objects that could be used as edges in the construction of polyhedra are toothpicks and pipe cleaners.
(b) In constructing polyhedra, students will practice identifying the different types of polyhedra and discover Euler’s formula, which say that the
number of faces of a polyhedron plus the number of vertices is equal to
the number of edges plus 2