Which figure(s) below can have a triangle as a two-dimensional cross section? I. cone II. cylinder III. cube IV. square pyramid
Answer all 7 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. Utilize the information provided for each question to determine your answer. Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.
Triangle is the image of triangle after a dilation with a scale factor of and centered at point . Is triangle congruent to triangle ? Explain your answer.
Determine and state the area of triangle , whose vertices have coordinates , and .
A support wire reaches from the top of a pole to a clamp on the ground. The pole is perpendicular to the level ground and the clamp is 10 feet from the base of the pole. The support wire makes a angle with the ground. Find the length of the support wire to the nearest foot.
In the diagram below, circle has a radius of 10 .
If , find the area of shaded sector , in terms of .
On the set of axes below, .
Describe a sequence of rigid motions that maps onto .
In right triangle , altitude is drawn to hypotenuse , and .
Determine and state, to the nearest tenth, the length of .
Given circle with radius , use a compass and straightedge to construct an equilateral triangle inscribed in circle . [Leave all construction marks.]
Which figure can have the same cross section as a sphere?
A circle is continuously rotated about its diameter. Which three-dimensional object will be formed?
If a rectangle is continuously rotated around one of its sides, what is the three-dimensional figure formed?
A right cylinder is cut parallel to its base. The shape of this cross section is a
An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a
In isosceles triangle shown below, , and altitude is drawn. The length of is 12 cm and the length of is 10 cm. Determine and state, to the nearest cubic centimeter, the volume of the solid formed by continuously rotating about .
Determine and state, to the nearest cubic centimeter, the volume of the solid formed by continuously rotating about .
In right triangle shown below, , and .
Determine and state, to the nearest tenth, the volume of the three-dimensional solid formed by rotating continuously around .
Determine and state, to the nearest tenth, the volume of the three-dimensional solid formed by rotating continuously around .
An isosceles right triangle whose legs measure 6 is continuously rotated about one of its legs to form a three-dimensional object. The three-dimensional object is a