Name: _______________________________________ Date: _____________Day 13: Three-Dimensional Review 36 points CC Geometry M3

Opening Exercise:Area of a Triangle Area of a Parallelogram Area of a Circle Circumference of a Circle

General Prisms Cylinders Pyramids Cones Spheres Density(Not on reference sheet)

For #1-4 Describe the solid that is formed by rotating each of these figures about line m and sketch it.1. 2. 3. 4.

For #5-9 identify the shape formed by a cross-section cut parallel to and perpendicular to the base.

SHAPE5. Cylinder 6. Sphere 7. Square

Pyramid8. Rectangular Prism

9. Cone

a. What shape is formed when a cross-section is cut parallel to the base?

(no base-so any cross-section)

b. What shape is formed when a cross-section is cut perpendicular to the base?

(no base-so any cross-section)

10. Given a right circular cylinder with a radius of 8 inches and a height of 20 inches. Which of the following choices is NOT a possible cross section of this cylinder?

1) Circle2) Oval3) Square4) Rectangle

11. Which 2-D shape could be revolved about the vertical line to create the 3-D solid shown at the right?

(1) (2) (3) (4)

1

mm m

12. Molly wishes to make a lawn ornament in the form of a solid sphere. The clay being used to make the sphere weighs .075 pound per cubic inch. If the sphere’s radius is 4 inches, what is the weight of the sphere, to the nearest pound?

1)342) 203) 154) 4

13. Luis is going to paint a basketball court on his driveway, as shown in the diagram below. This basketball court consists of a rectangle and a semicircle. Which expression represents the area of this basketball court, in square feet?

1) 802) 80 + 8π3) 80 + 16π4) 80 + 64π

14. Many of the ancient pyramids of Egypt are still buried in the sand. Satellites can now locate some of these buried structures using infrared technology. One of the buried pyramids has a square base with a height of 250 feet and volume of 9,633,333 cubic feet. Find the length of one side of the base to the nearest foot

1) 340 feet2) 115600 feet3) 196 feet4) 19267 feet

15. A square pyramid of solid gold has a base edge length of 5cm, altitude of 6cm, and a mass of 942 g, find the density of the gold to the nearest tenth.

16. Two stacks of 17 discs each are shown below. One stack forms a right rectangular prism but the other stack does not. Use Cavalieri’s principle to explain why the volumes of these two stacks of discs are equal.

2

17. To the nearest cubic centimeter, what is the minimum volume of the cylindrical can that holds a stack of 2 spheres with diameters of 24 cm each?

18. Find the volume of the cone with a radius of 3 cm and an angle of 53.1o, to the nearest cubic centimeter.

19. Rice falling from an open bag piles up into a figure conical in shape with an approximate circumference of 15 .70796 cm and an altitude of 8.66 cm. Use modeling to approximate how much rice, to the nearest cubic centimeter, creates this pile. Justify your answer.

20. A machine part is manufactured from a block of iron with circular cylindrical slots. The block of iron has a width of .14m, a height of .16m., and a length of .20m. If the density of iron is 7.87 g/cm3 what is the mass of the machine part to the nearest tenth of a gram.

3

21. A hemisphere sits centered atop a closed right circular cylinder. The radius of the hemisphere is 5 inches. The radius of the cylinder is 7 inches and its height is 6 inches.a) Find the volume of the solid to the nearest cubic inch.

b) If the solid takes 5 hours to fill with water. At what rate, in cubic inches per hour, is this solid being filled.

c) If there are 231 cubic inches in a liquid gallon, and the cost to fill this solid is $4.16 per gallon, how much does it cost to fill this solid? Round your answer to the nearest cent.

22. The three solids shown above have the same height and matching cross sectional areas parallel to the bases. Which of the solids have the same volume based on Cavalieri’s Principle?

1) A and B2) A and C3) B and C4) A, B and C

23. A wooden cube has an edge length of 4 centimeters and a mass of 23.872 grams. Determine the density of the cube, to the nearest thousandth. State which type of wood the cube is made of, using the density table below.

4