Section 1.3 Applications to Geometry and Literal Equations 71 Calculator Connections Topic: Using the Key The key on the calculator can also be used in the calculation Answers 3. 4. 3.14 5. h S V p 4r 2 pr 2 for Example 3(b). p P Solution: a. C 2pr C 2p C 2p r C 2p 880 ft 213.142 r p b. Substitute 880 ft for C and 3.14 for . The radius is approximately 140 ft. The diameter is twice the radius . Therefore, the diameter is 280 ft. Skill Practice The formula to compute the surface area S of a sphere is given by S 4pr 2. 3. Solve the equation for . 4. A sphere has a surface area of 113 in.2 and a radius of 3 in. Use the formula found in part (a) to approximate . Round to two decimal places. Solving a Literal Equation Example 4 The formula to find the area of a trapezoid is given by where b1 and b2 are the lengths of the parallel A 12 1b1 b22h, sides and h is the height. (See Figure 1-4.) Solve this formula for b1. Solution: The goal is to isolate b1. Multiply by 2 to clear fractions. Apply the distributive property. Subtract b2h from both sides. Divide by h. A 12 1b1 b22h 2A 2 12 1b1 b22h 2A 1b1 b22h 2A b1h b2h 2A b2h b1h 2A b2h h 2A b2h h b1h h b1 Skill Practice 5. The formula for the volume of a right circular cylinder is V pr 2h. Solve for h. p p 1d 2r2 140 ft r 2pr 2p b2 b1 h Figure 1-4 r h
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