3.16 Chapter 6 Geometry How much larger is the side of a square circumscribing a circle 155 cm in diameter than a square inscribed in the same circle, Fig. 6-72? 8. The radius of a circle is 5.00 m. Find the diameter of another circle containing 4 times the area of the first. 9. Find the distance x in Fig. 6-73. 10. In Fig. 6-74, distance OP is 8.65 units. Find the distance PQ. 11. Figure 6-75 shows a semicircle with a diameter of 105. Find distance PQ. Applications 12. In a park is a circular fountain whose basin is 22.5 m in circumference. What is the diameter of the basin? 13. The area of the bottom of a circular pan is 196 in.². What is its diameter? 14. Find the diameter of a circular solar pond that has an area of 125 m². 15. What is the circumference of a circular lake 33.0 m in diameter? 16. The distance around a circular park is 2.50 mi. How many acres does it contain? (1 sq. mi = 640 acres) 17. A woodcutter uses a tape measure and finds the circumference of a tree to be 95.0 in. Assuming the tree cross-section to be circular, what length of chain- saw bar is needed to fell the tree? (By cutting from both sides, one can fell a tree whose diameter is twice the length of the chain-saw bar.) 18. What must be the diameter d of a cylindrical piston so that a pressure of 125 lb/in.² on its circular end will result in a total force of 3610 lb? Hint: The f a surface is equal to the area of that surface times the pressure on that surface. 19. Find the length of belt needed to connect the three 15.0-cm-diameter pulleys in Fig. 6-76. Hint: The total curved portion of the belt is equal to the circum- ference of one pulley. 6.35 diameter FIGURE 6-74 P 60° 95.0 FIGURE 6-75

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A: Please see the below picture for detailed solution.

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