Download Student Name

Student Name: ______________________
Teacher:
______________________
District:
Miami-Dade County Public Schools
Assessment:
9_12 Mathematics Geometry Exam 3
Description:
Geometry Topic 7: 3-Dimensional Shapes
Form:
201
Date: ___________
1. A plane passes through the apex (top point) of a cone and then through its base. What geometric figure will be formed
from this intersection?
A.
square
B.
triangle
C.
parabola
D.
straight line
2. Which phrase describes a possible intersection of a plane with a double cone?
A.
two lines
B.
two points
C.
two circles
D.
two ellipses
3. The volume of the given cylinder is 282.74 cubic units.
Which is closest to the radius, r, of the base in units?
A.
1.69
B.
3.00
C.
6.00
D.
9.42
4. Sam works at an ice cream store and sells ice cream cookie sandwiches that are 0.25 inches thick and have a 3 inch
diameter. They are filled with ice cream that is 0.75 inches high and reaches to 0.25 inches away from the edge of the
cookie. What is the volume of each ice cream sandwich?
A.
3.67 cubic inches
B.
5.45 cubic inches
C.
7.21 cubic inches
D.
7.98 cubic inches
5. Jordan wants to prove the formula for the volume of the pyramid below by inserting the pyramid into a rectangular
prism.
Into which rectangular prism should Jordan insert the pyramid?
A.
B.
C.
D.
6. Two vases have the same height but are shaped differently as shown below.
How could the vases be sliced to use Cavalieri's principle to show that their volumes are
equivalent?
A.
B.
7. Consider this proof:
Which reason could be used to justify Statement 3 in this proof?
A.
subtraction property of equality
B.
substitution property of equality
C.
definition of supplementary
D.
definition of complementary
8. A truck hauled 136 cubic feet of sand to a construction site. The sand is dumped into a cone-shaped pile 6 feet in
height. What is the approximate diameter of the pile of sand, in feet?
A.
4.7
B.
9.3
C.
45.3
D.
68.0
9. Stan wants to double the volume of the jar shown below.
Which operation would accomplish this?
A.
doubling the height
B.
doubling the diameter
C.
doubling the height and diameter
D.
halving the diameter and quadrupling the height
10. Margaret is using a hollow cone and a hollow cylinder to determine how the volume of a
cone relates to the volume of a cylinder. The heights and diameters of the bases of the
cone and the cylinder are equal. Margaret fills the cone completely with water and then
pours the water into the cylinder. What will she find?
A. The water fills
of the cylinder.
B.
The water fills
of the cylinder.
C.
The water will fill the cylinder to the top.
D. The water fills
of the cylinder.
11. Given: PQRS is a parallelogram; S, P, and T are collinear.
Prove: 1 4.
Statements
1. PQRS is a parallelogram; S, P, and T
are collinear
2.
3. 1 3
4.
5. 4
6. 1
3
4
Reasons
1. Given
2. Definition of a parallelogram
3. Parallel lines cut by a transversal form
congruent corresponding angles
4. Definition of a parallelogram
5. ?
6. Transitive property of congruence
Which reason could be used to justify Statement 5?
A.
Angles that are supplements of the same angle are congruent to each other.
B.
Parallel lines cut by a transversal form congruent alternate interior angles.
C.
Parallel lines cut by a transversal form congruent corresponding angles.
D.
Intersecting lines form congruent vertical angles.
12. A food company currently sells tomato juice in a cylindrical container with a diameter of 6
centimeters (cm) and a height of 10 cm. The company's marketing team suggests there
would be better sales if the container were a cone. What should the diameter of the
cone be if the company changes neither the height nor the volume? Round to the
nearest cm, if needed.
A.
5
B.
9
C.
11
D.
27
13. Which formula can be used to determine the volume of this 3-dimensional figure?
A.
B.
C.
D.
14. Monica lists the steps to prove that any point on the perpendicular bisector of a segment
is equidistant from the endpoints of the segment.
Which statement should Monica write in the blank in step 5?
A.
B.
C.
D.
15. The graph below shows a semicircle with a radius of 2 units.
About what line should the semicircle be revolved in order to create a sphere?
A.
the line y = 0
B.
the line x = 0
C.
the line x = 2
D.
the line y = 2
16. Max is planting four 20 foot tall palm trees alongside his house. Each tree will need a cylindrical hole that is 34 inches
in diameter and 28 inches deep to accommodate the roots. His trash hauler will only take away the excess dirt if it is
in rectangular bags that are 2 feet by 1.5 feet by four feet. However, Max can only fill the bags one third of the way
or they will be too heavy for him to move. How many bags will he have to buy so he can put all the dirt out for
pickup?
A.
5
B.
15
C.
24
D.
59
17. A plane intersects a cylinder without intersecting either of its bases. The plane is not parallel to the bases.
What geometric figure will be formed from this intersection?
A. a circle
B.
a square
C.
an ellipse
D. a line segment
18. A certain cylinder has a height of
and a certain square prism has a height of
The
circular cross section of the cylinder and the square cross section of the prism have the same
area. Which equation expresses the relationship of the volume of the cylinder,
to the
volume of the prism,
A.
B.
C.
D.
19. Sam wants to compare the volumes of the cone in Figure 1 and the square pyramid in Figure 3 below. The heights of
the cone and the pyramid are equal. The radius of the base of the cone and the length of the base of the pyramid are
given in centimeters (cm). When the cone is placed inside the pyramid, the base of the cone touches each edge of the
square base of the pyramid at one point, as shown in Figure 2.
The volume of the cone is 1884 cubic centimeters. What is the difference in the volume of the pyramid and the
volume of the cone, in cubic centimeters?
A.
400
B.
516
C.
7200
D.
7536
20. A line segment PQ has endpoint P at
endpoint of P' has coordinates
A.
B.
C.
D.
and Q at
As a result of dilation about the origin, the
What are the coordinates of Q'?
21. A rectangle will be rotated about Line L in the figure below.
What best describes the three-dimensional object formed by rotating the rectangle about Line L?
A.
solid cylinder
B.
solid rectangular prism
C.
rectangular prism with a square hole down its length
D. cylinder with a cylindrical hole down its length
22. The figures shown below all have circular bases with a radius of r units. The four figures
have equal heights.
Which figures, if any, have equal volumes?
A.
I and II; III and IV
B.
I and III; II and IV
C.
All of the figures have equal volume.
D.
No two figures have equal volume.
23.
What are the coordinates of
if the orgin is the center of dilation and the scale factor is
A.
B.
C.
D.
24. The endpoints of
are located at E (-4, -2) and F (2,3). What are the coordinates of point G, which divides
such
that EG : GF is equal to 1 : 3 ?
A.
(-2.5, -1)
B.
(-2.5, -0.75)
C.
(-1, 0.5)
D.
(0.5, 1.75)
25. The volume of a sphere is
of the new sphere?
A.
B.
C.
D.
cubic inches. If the radius of the sphere is doubled, what is the volume, in cubic inches,