Geometry Review 4/28/16
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1 Geometry Review 4/28/16 Name: Date: SHOW ALL YOUR WORK!!! Finish for homework! 1. A photograph 3 inches wide and 5 inches long is to be enlarged so that the length is 15 inches. The new width will be 3. The Rivera family bought a new tent for camping. Their old tent had equal sides of 10 feet and a floor width of 15 feet, as shown in the accompanying diagram. A. 9 in. B. 13 in. C. 17 in. D. 25 in. If the new tent is similar in shape to the old tent and has equal sides of 16 feet, how wide is the floor of the new tent? 2. The area of the rectangular playground enclosure at Happy Times Nursery School is 600 square meters. The length of the playground is 25 meters longer than the width. Find the dimensions of the playground. [Only an algebraic solution will be accepted.] 4. Frank, George, and Hernando are a plumber, a cabinet maker, and an electrician, though not necessarily in that order. Each can do all work appropriate to his own field, but no work in other fields. Frank was not able to install a new electric line in his home. Hernando was not able to make cabinets. George is also a building contractor who hired one of the other people to do his electrical work. Which statement must be true? A. Hernando is an electrician. B. George is a cabinet maker. C. Frank is a plumber. D. Frank is an electrician. page 1
2 5. An image of a building in a photograph is 6 centimeters wide and 11 centimeters tall. If the image is similar to the actual building and the actual building is 174 meters wide, how tall is the actual building, in meters? 8. José wants to build a triangular pen for his pet rabbit. He has three lengths of boards already cut that measure 7 feet, 8 feet, and 16 feet. Explain why José cannot construct a pen in the shape of a triangle with sides of 7 feet, 8 feet, and 16 feet. 6. A wheel has a radius of 5 feet. What is the minimum number of complete revolutions that the wheel must make to roll at least 1,000 feet? 9. The accompanying diagram shows the roof of a house that is in the shape of an isosceles triangle. The vertex angle formed at the peak of the roof is The accompanying diagram shows a football player crossing the 20-yard line at an angle of 30 and continuing along the same path. What is the measure of x? What is the measure of angle B, where the player crosses into the end zone? A. 138 B. 96 C. 84 D. 48 A. 30 B. 60 C. 150 D. 180 page 2 Geometry Review 4/28/16
3 10. Manuel plans to install a fence around the perimeter of his yard. His yard is shaped like a square and has an area of 40,000 square feet. The company that he hires charges $2.50 per foot for the fencing and $50.00 for the installation fee. What will be the cost of the fence, in dollars? 12. Oatmeal is packaged in a cylindrical container, as shown in the diagram below. The diameter of the container is 13 centimeters and its height is 24 centimeters. Determine, in the terms of π, the volume of the cylinder, in cubic centimeters. 11. The support beams on a bridge intersect in the pattern shown in the accompanying diagram. If AB and CD intersect at point E, m AED = 3x + 30, and m CEB = 7x 10, find the value of x. page 3 Geometry Review 4/28/16
4 13. A designer created a garden, as shown in the diagram below. The garden consists of four quarter-circles of equal size inside a square. The designer put a fence around both the inside and the outside of the garden. 14. Ross is installing edging around his pool, which consists of a rectangle and a semicircle, as shown in the diagram below. Which expression represents the amount of fencing, in yards, that the designer used for the fence? A π B π Determine the length of edging, to the nearest tenth of a foot, that Ross will need to go completely around the pool. C π D π page 4 Geometry Review 4/28/16
5 15. As shown in the diagram below, a landscaper uses a cylindrical lawn roller on a lawn. The roller has a radius of 9 inches and a width of 42 inches. 17. The diameter of the base of a right circular cylinder is 6 cm and its height is 15 cm. In square centimeters, the lateral area of the cylinder is A. 180π B. 135π C. 90π D. 45π To the nearest square inch, the area the roller covers in one complete rotation is 18. The diameter of a sphere is 5 inches. Determine and state the surface area of the sphere, to the nearest hundredth of a square inch. A. 2,374 B. 2,375 C. 10,682 D. 10, The lateral area of a right circular cone is equal to 120π cm 2. If the base of the cone has a diameter of 24 cm, what is the length of the slant height, in centimeters? A. 2.5 B. 5 C. 10 D If the surface area of a sphere is 144π square centimeters, what is the length of the diameter of the sphere, in centimeters? A. 36 B. 18 C. 12 D In a circle, the coordinates of the endpoints of a diameter are (4, 5) and (10, 1). What are the coordinates of the center of the circle? page 5 Geometry Review 4/28/16
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