424 CHAPTER 7 The Metric System Example 9 Measuring Medicine A nurse must give a patient 3 cc of the drug gentamicin mixed in 100 cc of a normal saline solution. a) How many milliliters of the drug will the nurse administer? b) What is the total volume of the drug and saline solution in milliliters? Solution a) Because 1 cc is equal in volume to 1 m , the nurse will administer 3 m of the drug. b) The total volume is 3 100, + or 103 cc, which is equal to 103 m . 7 Now try Exercise 75 Example 10 A Water Heater A water heater, in the shape of a right circular cylinder, has a radius of 50 cm and a height of 148 cm. What is the capacity, in liters, of the water heater? Solution The water heater is illustrated in Fig. 7.11. The formula for the volume of a right circular cylinder is V r h. 2 π = Since we want the capacity in liters, we will express all the measurements in meters. The volume will then be given in cubic meters, which can be easily converted to liters. Thus, 50 cm 0.5 m, = and 148 cm 1.48 m. = π π π = = = ≈ V r h (0.5 m) (1.48 m) (0.25)(1.48) 1.1624 m 2 2 3 We want the volume in liters, so we must change the answer from cubic meters to liters. 1 m 1000 3 = So, 1.1624 m 1.1624 1000 1162.4 3 = × = Therefore, the water heater’s capacity is about 1162.4 . 7 Now try Exercise 77 50 cm 148 cm Figure 7.11 Example 11 Comparing Volume Units a) How many times larger is a cubic meter than a cubic centimeter? b) How many times larger is a cubic dekameter than a cubic meter? Solution a) The procedure used to determine the answer is similar to that used in Example 3 in this section. First we draw a cubic meter, which is a cube 1 m long by 1 m wide by 1 m high. In Fig. 7.12, we represent each meter as 100 centimeters. The volume of the cube is its length times its width times its height, or V l w h 100 cm 100 cm 100 cm 1 000 000 cm3 = × × = × × = 1 m 100 cm 1 m 100 cm 100 cm 1 m Figure 7.12 MATHEMATICS TODAY Metrics and Medicine Both milliliters and cubic centimeters are commonly used in medicine. In the United States, cubic centimeters are commonly denoted cc rather than the cm3 used in the metric system. A patient’s intake and output of fluids and intravenous injections are commonly measured in cubic centimeters. Drug dosage is measured in milliliters. The following question is from a nursing exam. Can you determine the correct answer? In caring for a patient after delivery, you are to give 12 units of Pitocin (in 1000 cc of intravenous fluid). The ampule is labeled 10 units per m 0.5 . How much of the solution would you draw and give? a) 0.6 cc b) 1.2 cc c) 6.0 cc d) 9.6 cc The answer is upside down below. Answer: (a) Why This Is Important Our health is important to us. The vitamins and minerals we take, as well as prescription drugs, are often given in metric units.
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