Math 8 Study Guide Name ___________________________________ Unit 3: Geometric Applications of Exponents 1. 2. 3. The Pythagorean Theorem states that the ___________ of the length of the ___________________ is equal to the _________ of the __________ of the lengths of the _______________. The Pythagorean Theorem can be represented by the equation ____________________, where a and b are the length of the ____________ of the triangle, and c is the length of the _____________. Use what you know about the Pythagorean Theorem to label the sides of the following triangle. 4. Is a triangle with the lengths 7, 24, and 25 a right triangle. Why or why not. Show work to indicate how you got your answer. 5. A football field is 360 feet by 45 feet. How long is the walk from one corner diagonally to the opposite corner? 6. Using the illustration below, what is the approximate height of the hot air balloon? Date ________________ 7. A rectangle has a diagonal 25 inches long and a width of 6 inches. What is the length of the rectangle? 8. Which of the following measures are valid measures of the sides of a right triangle? Explain your reasoning. A. 3, 4, 7 B. 5, 12, 13 C. 20, 21, 28 D. 12, 37, 34 9. A spider has taken up residence in a small cardboard box which measures 2 inches by 4 inches by 4 inches. What is the length, in inches, of a straight spider web that will carry the spider from the lower right front corner of the box to the upper left back corner of the box? 10. A package is in the shape of a cube. The height if the package is 10 inches. What is the diagonal length of the package? 11. Find the length of the missing side. 18. A party hat is in the shape of a cone with a radius of 3 in. and a height of 5 in. What is the volume of the party hat? X 3 in. 19. What is the volume of a beach ball with a radius of 12 centimeters? 5 in. 20. What is the volume of the following cone? 10 mm 12. Solve for y: 2𝑦 3 = 16 5 mm 13. Solve for z: 3𝑧 2 = 108 14. Explain what the word volume means. 21. Find the volume of the sphere shown below. Radius is 2in 15. How does the volume of a cylinder compare to the volume of a cone? 16. How does the volume of a cylinder and cone compare to the volume of a sphere? 22. Find the volume of the cylinder below. 7 in 5 in 17. A candle maker uses a cylinder mold, which is 18 inches tall and has a radius of 1 inch. What is the volume of the candle mold? 23. The volume of a cylinder is 12.56 𝑚3 . If the height of the cylinder is 1 m, what is its diameter? 26. What is the distance between P1 and P2? 24. What are the two methods of finding the distance between two points? 25. What is the distance between P1 and P2? 27. Given points C(-6, 10) and D(-3, -2), what is the length of CD? 28. Given points S(-4, -2 and T(-1, 0), what is the length of ST?
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