V cylinder = V cone = V sphere =
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1 Math 7-8 Study Guide Benchmark 2 & Fluency Test Know the formulas for Volume of Cylinders, Cones, and Spheres & be able to use them to solve real world mathematical problems. V cylinder = V cone = V sphere = 1-4. Solve the equation. Check your solution. 1. 8p 47 15p x 2. 6 f 1511f 25 x. 4 5d 8d 14 2x 4. 2k 22 8( k 1) 5. Find the perimeter of the square. 11. Find the circumference of the circle. 22 Use.14 or for 7 9 in. 6. Twenty-five more than 5 times the quantity of a number decreased by 7 is 0. Find the number. 7. The measures of two supplementary angles have a ratio of 5:4. What is the measure of the larger angle? Find the value of x. 12. Find the area of the semicircle. 55 cm 8. x A circular clock on the outside of a building covers an area of square feet. What is the diameter of the clock? Use.14 for A cylindrical swimming pool has a diameter 2 of feet and a height of 7 feet. About how many gallons of water can the pool contain? Round your answer to the nearest whole number. (1 ft 7.5 gal) x
2 15. Find the height of the cone if the volume is 10 mm. Round your answer to the nearest tenth millimeter. 16. The cooler contains 10 grape juice bottles and 15 cranberry juice bottles. You randomly choose two bottles. What is the probability that both bottles are cranberry juice? 17. You flip a coin & you roll a number cube. What is the probability that you flip heads & roll a number less than? 18. Trapezoids ABCD and EFGH are congruent. If the perimeter of trapezoid ABCD is 0cm, what is the length of side GF? Use the figure to the right. a b 19. If the measure of = 122, then the measure of 6 =?. 20. If the measure of 4 = 56, then the measure of 5 =?. t Find the volume. Round your answer to the nearest tenth ft 16 in. 12 ft Solve the inequality. Graph the solution. 8 in x m w (x 2) 5 4
3 28. An isosceles triangle has a base of 5 centimeters and legs x centimeters long. The perimeter is no more than 0 centimeters. Write and solve an inequality to find the possible values of x. Find the value of x. Then classify the triangle Find the surface area and volume of the prism You spin the spinner twice. Find the probability of the event.. Describe the likelihood of spinning an odd number then an even number. 4. The double box-and-whisker plot shows the numbers of correct answers on a test for each student in Room 212 and Room 214. a. Compare the populations using measures of center and variation. b. Express the difference in the measures of center as a multiple of each measure of variation. 5. The shaded figure is congruent to the nonshaded figure. Describe two different sequences of transformations in which the nonshaded figure is the image of the shaded figure. 6. The vertices of a triangle are A(-2, 4), B(1, 2) and C(-2, -2). Reflect the triangle in the y-axis, and then rotate the image 90 counterclockwise about the origin. What are the coordinates of the image? 7. The polygons are similar. Find x.
4 Complete the statement using the figure to the right. Explain your reasoning. 8. If the measure of 46, then the measure of 6?. 9. If the measure of 5 102, then the measure of 8?. 40. If the measure of 4 98, then the measure of 7?. 41. If the measure of 6 59, then the measure of 4?. 42. Find the perimeter of the semicircle. 4. You want to find the diameter of a large circular fountain in the park, but cannot measure straight across. Explain how you could use the circumference of the fountain to estimate the diameter. Determine whether the sample is biased or unbiased. Explain. 44. You want to estimate the number of students in your grade who choose math as their favorite subject. You survey 10 of your close friends. 45. You want to estimate the number of people in a town in favor of a proposed curfew law. You survey every fifth person who enters a post office. Use the figure to the right. 46. What is the measure of What is the value of x?
5 Math 7-8 Study Guide Placement & Fluency Test Answer Section V cylinder= V cone= V sphere= r 2 h 1 r 2 h 4 r 1. ANS: 2. ANS:. ANS: 4. ANS: 5. ANS: 156 in. 6. ANS: 7. ANS: ANS: ANS: ANS: ANS: about in. 12. ANS: 1. ANS: 8 ft 14. ANS: 42, 202 gal (if using.14), 42,240 gal (if using 22/7) 15. ANS: ANS: 7/ ANS: 1/6 18. ANS: 9 cm 19. ANS: ANS: ANS: 22. ANS: ANS: in. 24. ANS: 25. ANS: 26. ANS: 27. ANS: 28. ANS:, 29. ANS: ; acute scalene 0. ANS: ; right isosceles 1. ANS: 94 ft ; 60 ft BNK: Chapter 14 - Surface Area and Volume 2. ANS: 96 cm ; 42 cm BNK: Chapter 14 - Surface Area and Volume. ANS: unlikely
6 4. ANS: a. The median and IQR of Room 212, 20 and 2, are less than the median and IQR of Room 214, 22 and. b. The difference in the medians is about 0.67 to 1 times the IQR. 5. ANS: Sample answer: 1) rotate 90 counterclockwise about the origin, translate 1 unit down 2) translate 1 unit left, rotate 90 counterclockwise about the origin 6. ANS: 7. ANS: 8. ANS: and are alternate interior angles. 9. ANS: and are vertical angles. 40. ANS: 82; Sample answer: 4 and are alternate interior angles, and and are supplementary. 41. ANS: 121; Sample answer: 4 and are supplementary, and and are alternate interior angles. 42. ANS: about 0.84 mi 4. ANS: Measure the circumference, then use the formula. Divide the circumference by.14 to estimate the diameter. 44. ANS: biased; The sample is not representative of the population because close friends are more likely to have the same opinions. 45. ANS: unbiased; The sample is representative of the population and selected at random. 46. ANS: 15 o 47. ANS: 20
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