Unit 5 Test Review: Modeling with Geometry Honors

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1 Name: ate: 1. What is the volume, in cubic centimeters, of a cube whose edge measures 2 centimeters? 5. A right circular cylinder has a base whose area is 12π. If the height of the cylinder is 6, the volume of the cylinder is A. 18π B. 24π. 36π. 72π 2. The volume of a rectangular solid is 180 cubic centimeters. The length is 10 centimeters and the width is 4 centimeters. Using the formula V = lwh, find the number of centimeters in the height. 6. The volume of a rectangular solid is 80 cubic centimeters, the length is 2 centimeters, and the width is 4 centimeters. Find the number of centimeters in the height of the rectangular solid. 3. If the volume of a cube is 64 cubic centimeters, how many centimeters are in the length of an edge of the cube? 7. The volume of a cube is 64 cubic inches. Its total surface area, in square inches, is A. 16 B A side of a cube measures 4 centimeters and a side of a smaller cube measures 2 centimeters. The volume of the larger cube is how many times the volume of the smaller cube? A. 6 B A fish tank with a rectangular base has a volume of 3,360 cubic inches. The length and width of the tank are 14 inches and 12 inches, respectively. Find the height, in inches, of the tank. page 1

2 9. Which diagram represents the figure with the greatest volume? A. B. 11. The volume of a cylindrical can is 32π cubic inches. If the height of the can is 2 inches, what is its radius, in inches? A. 8 B A cylinder has a diameter of 10 inches and a height of 2.3 inches. What is the volume of this cylinder, to the nearest tenth of a cubic inch? A B A storage container in the shape of a right circular cylinder is shown in the accompanying diagram. 13. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches. What is the volume of this container, to the nearest hundredth? A in 3 B in in in 3 What is the volume of the cone to the nearest cubic inch? A. 201 B page 2

3 14. A regular pyramid with a square base is shown in the diagram below. 17. A packing carton in the shape of a triangular prism is shown in the diagram below. A side, s, of the base of the pyramid is 12 meters, and the height, h, is 42 meters. What is the volume of the pyramid in cubic meters? What is the volume, in cubic inches, of this carton? A. 20 B If the surface area of a sphere is represented by 144π, what is the volume in terms of π? A. 36π B. 48π. 216π. 288π 18. A sphere has a diameter of 18 meters. Find the volume of the sphere, in cubic meters, in terms of π. 16. The volume, in cubic centimeters, of a sphere whose diameter is 6 centimeters is A. 12π B. 36π. 48π. 288π 19. The volume of a sphere is approximately cubic centimeters. What is the radius of the sphere, to the nearest tenth of a centimeter? A. 2.2 B page 3

4 20. In the accompanying diagram, AB, EF intersects AB at E and at F, and GH intersects AB at G and EF at H. If m EGH = 40, m GHE = 80, and m EF = x, what is the value of x? 23. In the accompanying figure, WX YZ; AB and intersect WX at E and YZ at F and G, respectively. If m EW = m BEX = 50, find m EGF. 21. In the accompanying diagram, H EF. If m HF = 30 and m EF = 55, find m E. 24. In the accompanying diagram, AB E, m FE = 25, m FE = 130, and m AB = x. What is the value of x? 22. In the accompanying diagram, AB is a parallel to, m BA = 46, and m B = 65. Find the measure of AB. 25. In the accompanying diagram, AB and intersect at E. Angles AE and EB measure 2x 6 and 6x 50, respectively. Find the value of x. page 4

5 26. In the accompanying diagram, AB and intersect at E, and m AE = 57. If m EB = 3x + 15, find the value of x. 29. In the accompanying diagram, the adjacent angles formed by intersecting lines AB and have measures of 3x + 50 and x Find x. 27. In the accompanying diagram, AB and intersect at E, and m AE = 3x If m EB = 2x + 50, find the value of x. 30. Lines AB and intersect at E, m AE = 110, m EB = 3x + 2y, m BE = 9x + y, and m EA = 70. Find the values of x and y. heck your answer. [Only an algebraic solution will be accepted.] 28. In the accompanying diagram, AB is a straight line. m AB = 8x, and m B = x Find x. 31. In the accompanying diagram, m EB = 6x, m E = 3x 11, and m B = 74. What is the value of x? page 5

6 32. In the accompanying diagram, AOB is a straight line, m AO = 5x, m O = 3x + 30, and m OB = 2x Find the value of x. 34. In the accompanying diagram of rectangle AB, A = 12 and AB = 5. What is the length of diagonal A? 33. In the accompanying diagram, AB is a rectangle. If B = 26 and = 24, find B. 35. In rectangle MATH, AT = 8 and TH = 12. Find the length of diagonal HA to the nearest tenth. page 6

7 Problem-Attic format version c EducAide Software Licensed for use by soliver@wcpss.net Terms of Use at 11/27/ A A B 972 π A x = 10, y =

Quads. 4. In the accompanying figure, ABCD is a parallelogram, m A = 2x + 35, and m C = 5x 22. Find the value of x.

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