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?

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1 Student Name: Teacher: Date: District: Description: Miami-Dade County Public Schools Geometry Topic 7: 3-Dimensional Shapes 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? square triangle parabola straight line 2. Which phrase describes a possible intersection of a plane with a double cone? two lines two points two circles two ellipses 3. The volume of the given cylinder is cubic units. Which is closest to the radius, r, of the base in units?

2 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? 3.67 cubic inches 5.45 cubic inches 7.21 cubic inches 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?

3 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?

4 7. Consider this proof: Which reason could be used to justify Statement 3 in this proof? subtraction property of equality substitution property of equality definition of supplementary 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? Stan wants to double the volume of the jar shown below.

5 Which operation would accomplish this? doubling the height doubling the diameter doubling the height and diameter 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? The water fills of the cylinder. The water fills of the cylinder. The water will fill the cylinder to the top. The water fills of the cylinder. 11. Given: PQRS is a parallelogram; S, P, and T are collinear. Prove: 1 4. Statements Reasons 1. PQRS is a parallelogram; S, P, and T 1. Given are collinear Definition of a parallelogram Parallel lines cut by a transversal form congruent corresponding angles Definition of a parallelogram ? Transitive property of congruence Which reason could be used to justify Statement 5? Angles that are supplements of the same angle are congruent to each other. Parallel lines cut by a transversal form congruent alternate interior angles. Parallel lines cut by a transversal form congruent corresponding angles. Intersecting lines form congruent vertical angles.

6 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 Which formula can be used to determine the volume of this 3-dimensional figure?

7 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? 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? the line y = 0 the line x = 0 the line x = 2 the line y = 2

8 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 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 circle a square an ellipse 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,

9 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 line segment PQ has endpoint P at and Q at As a result of dilation about the origin, the endpoint of P' has coordinates 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? solid cylinder solid rectangular prism rectangular prism with a square hole down its length cylinder with a cylindrical hole down its length

10 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? I and II; III and IV I and III; II and IV All of the figures have equal volume. 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?

11 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? (-2.5, -1) (-2.5, -0.75) (-1, 0.5) (0.5, 1.75) 25. The volume of a sphere is cubic inches. If the radius of the sphere is doubled, what is the volume, in cubic inches, of the new sphere?