WVDE Math 7 G Solve Real-life and Mathematical Problems involving Angle Measure, Area, Surface Area, and Volume Test

Transcription

1 WVDE Math 7 G Solve Real-life and Mathematical Problems involving Angle Measure, Area, Surface Area, and Volume Test 1

2 General Offline Instructions: Read each question carefully and decide which answer is correct. 2

3 1. The figure above is a square with four congruent parallelograms inside. What is the area, in square units, of the shaded portion? A 60 B 84 C 114 D A circular area with a diameter of 10 feet has a circumference of 31.4 feet. A rectangle that is 8 feet by 7.7 feet has a perimeter of 31.4 feet. Does the circle or the rectangle have more area? A They both have the same area. B The circle has more area. C The rectangle has more area. D There is not enough information to find out. 3

4 3. Mr. Jones has a pool that is 15 feet long and 9 feet wide. He wants to put a 3-foot wide concrete walkway around the pool. If the concrete will cost him $4.30 for each square foot of the walkway, what will be the price of the concrete? A $774 B $ C $459 D $ Two angles are complementary. One angle is 5 times greater than the other. What is the measure of the larger angle? A 15 degrees B 30 degrees C 75 degrees D 150 degrees 4

5 5. The ferris wheel at the West Virginia State Fair in Fairlea has a diameter of 250 ft. Use 3.14 for pi. What is the distance for one complete revolution? A B C D 393 ft 785 ft 1,570 ft 49,063 ft 5

6 6. You are painting a chemical storage container as shown. Since the storage container is already in place, you do not paint the bottom face. The paint used costs $32 per gallon and covers 18 square meters. What is the approximate cost of the paint needed to paint this container? A $391 B $459 C $528 D $684 6

7 7. The backdrop for your class play is shaped like the figure shown. Which of these is the area of the shaded region? A 42 square meters B 48 square meters C square meters D square meters 8. A contractor is building a patio in the shape of a rectangle and isosceles trapezoid with the dimensions shown. How much will it cost to build the patio if the contractor charges $15 per square foot? A $3,600 B $3,420 C $915 D $900 7

8 9. Mr. Robles is building a dog pen in the shape of circle in his backyard. The pen has a radius of 20 feet. The fencing that Mr. Robles normally buys cost $2.80 a foot, but it is currently on sale at 25% off. (Use 3.14 for π.) What will be the approximate cost of the fencing? A $350 B $130 C $95 D $ You measure the dimensions of a gift box with a ruler. The dimensions are inches wide, inches long and inches tall. Your teacher asks you to estimate the volume of the box. Which method will provide the closest estimate of the volume of the box? A Round all of the measurements to the nearest whole number and multiply the three values together. B Use and round the other measurements to the nearest whole number and multiply the three values together. C Round to and the other measurements to the nearest whole number and multiply the three values together. D Round all measurements to the lowest whole number and multiply the three values together. 8

9 11. Terri needs to put a sealant on one of her chemical storage unit are shown below. The sealant cost $35 a gallon and covers 12 square meters. The storage unit will not be sealed on its bottom. How much will it cost to seal the storage container? A $ B $ C $ D $

10 12. Billy needs to fertilize his garden. In order to make sure Billy buys the right amount of bags, he needs to find the area of his garden pictured below. Using the figure, find the area of Billy's garden. A 180 square feet B 1900 square feet C 2100 square feet D 2600 square feet 10

11 13. The diagram shows the 4th hole of a miniature golf course that is under construction. The 4th hole will be covered with artificial turf that costs $0.48 per square foot. What is the approximate cost of artificial turf for the 4th hole? Use 3.14 for π. A $30 B $180 C $200 D $ If the diameter of a circle is doubled, how would this affect the circumference and area? A The circumference and area would double. B The circumference and area would be 4 times greater. C The circumference would double and the area would be 4 times greater. D The area would double and the circumference would be 4 times greater. 11

12 15. Shawna is building a model sand castle using the shapes shown. Which statement is true about the volume of the two shapes? A The pyramid has a larger volume by approximately 270 cm 3 B The rectangular prism has a larger volume by approximately 270 cm 2 C The pyramid has a larger volume by approximately 90 cm 3 D The rectangular solid has a larger volume by approximately 90 cm 3 12

13 16. Two angles are complementary. One angle is 8 times greater than the other. What is the measure of the larger angle? A 10 degrees B 20 degrees C 80 degrees D 160 degrees 17. Two angles are complementary. One angle is 5 times greater than the other. What is the measure of the larger angle? A 15 degrees B 30 degrees C 75 degrees D 150 degrees 18. Bob wants to build a dog pen with the largest area possible. He has only 28 yards of fencing. Which of the following dimensions should he use for his rectangular pen? A 4 yds by 7 yds B 5 yds by 9 yds C 7 yds by 7 yds D 1 yd by 13 yds 13

14 19. A square archery target inscribes a circle as shown in the figure below. Elaine would like to know the shaded area that is inside the square and outside the circle. What is the least amount of measurements that Elaine will have to take to find this area? A Elaine needs to measure the length of one side of the square and the radius of the circle. B Elaine needs to measure the length of one side of the square. C Elaine needs to measure the length of one side and the diagonal of the square. D It is impossible to determine the area of the shaded region. 20. Timothy is designing a game board to be used in math classrooms to study polygons. He would like to make a board in the shape of a regular polygon with each interior angle measuring 144 o. How many sides would the board have? A 10 sides B 12 sides C 34 sides D 36 sides 14

15 21. Bill has 80 feet of fencing to enclose a rectangular corral for his horse. He wants his horse to have the largest area possible. Which of the following dimensions should he use? A 80 ft by 1 ft B 30 ft by 10 ft C 20 ft by 20 ft D 10 ft by 8 ft 22. What is the area of the figure? A 60 in 2 B 54 in 2 C 34 in 2 D 42 in 2 15

16 23. What is the area of the figure? A 36 in 2 B 48 in 2 C 30 in 2 D 42 in What is the area of the figure? A 216 ft 2 B 120 ft 2 C 58 ft 2 D 96 ft 2 16

17 25. What is the area of the figure? A 120 m 2 B 78 m 2 C 43 m 2 D 63 m You need to determine the number of 1-inch tiles to put around the edge of your new pool. The pool is a rectangle with two semicircular ends as shown. Approximately how many tiles will you need? A 117 tiles B 174 tiles C 1399 tiles D 1831 tiles 17

18 27. You and your friend are planning to paint the exterior walls of your country farmhouse (all vertical surfaces). The paint you like best cost $25 per gallon and covers 250 square feet per gallon. All measurements are in feet. How many gallons of paint are needed to paint the walls? A 7 gallons B 8 gallons C 15 gallons D 16 gallons 28. Lines m and n represent two roads meeting at an intersection C. The intersection of the roads forms angles of 120 o and x o respectively. If the roads meet at angles 120 o and x o, which statement about the angles could always be true? A The two angles are congruent and supplementary. B The two angles are vertical and supplementary. C One of the two angles is a right angle. D The two angles form a straight angle and are supplementary. 18

19 29. A carpenter has been hired to cover a 12-foot by 14-foot kitchen with an arrangement of 2-inch square tiles along the outside edges of the floor and 8-inch square tiles for the rest of the floor. The 8-inch square tiles come 24 in a box and the 2-inch square tiles come 48 in a box. What is the minimum number of boxes of each type of tile needed for the job? A 15 boxes of 8-inch tiles and 7 boxes of 2-inch tiles B 3 boxes of 8-inch tiles and 2 boxes of 2-inch tiles C 16 boxes of 8-inch tiles and 7 boxes of 2-inch tiles D 3 boxes of 8-inch tiles and 1 box of 2- inch tiles 30. Ginger is opening a gift box. She wonders, "What could come in this box?" Which is the best estimate of the volume of the box? A 30 cubic centimeters B 900 cubic centimeters C 8,000 cubic centimeters D 27,000 cubic centimeters The box measures 28 centimeters on each side. 31. What is the area of the city inside the path ran by Melissa? A B C D 19

20 32. You need to build a window frame for a regular octagonal window. To make the frame, you ll cut identical trapezoidal pieces. What are the measures of the angles of the trapezoid? A 22.5 degrees and degrees B 45 degrees and 135 degrees C 67.5 degrees and degrees D 75 degrees and 105 degrees 20

21 33. As a school improvement project, the student council is building a circular flowerbed around the flagpole at the front of the building. The flower bed is to have white carnations 5 feet out from the pole on all sides and red roses extending an additional 6 feet beyond the white carnations. Which method correctly determines the amount of fencing needed to enclose the flowerbed? A Multiply the radius of the white flowerbed by multiply the width of the red flowerbed by and add the results together. B Add the radius of the white flower bed to the width of the red flower bed and multiply the result by C Add the radius of the white flower bed to the width of the red flower bed, square the result and multiply by D Multiply the radius of the white flowerbed by multiply the width of the red flower bed by and add the results together. 34. Look at the two circles drawn below. Which statement is true about the ratio of for the circles shown? A The ratio for circle A is greater than the ratio for circle B. B The ratio for circle A is less than the ratio for circle B. C The ratio for both circles is equal to D The ratio for both circles is equal to 21

22 35. An architect is designing a new swimming pool for a park in your town. What is the approximate area of the pool if all of the measurements are in meters? A 167 square meters B 207 square meters C 285 square meters D 442 square meters 36. The roof on your house is formed by two congruent trapezoids and 2 congruent isosceles triangles. You want to put new shingles on your roof. Each shingle will cover 0.25 square foot of area. How many shingles should you buy? A 225 shingles B 900 shingles C 1800 shingles D 3600 shingles 22