Digital SATMath: AlgebraEasy
A landscaper is designing a circular garden. The area of the garden, A, in square feet, is given by the formula A = πr², where r is the radius in feet. If the landscaper wants the area to be 153.86 square feet, what should be the radius of the garden? (Use π ≈ 3.14)
- A8 feet
- B7 feet
- C6 feet
- D5 feet
Show answer & explanationAnswer & explanation
Correct answer: B. 7 feet
Given the area A = 153.86 ft² and the formula A = πr². Substitute the given values: 153.86 = 3.14 * r². Divide both sides by 3.14: r² = 153.86 / 3.14 = 49. Take the square root of both sides: r = √49 = 7. The radius of the garden should be 7 feet.
Why the other options are wrong
- A. Incorrect. If r=8, A = 3.14 * 64 = 200.96.
- C. Incorrect. If r=6, A = 3.14 * 36 = 113.04.
- D. Incorrect. If r=5, A = 3.14 * 25 = 78.5.
Solving for a Variable in a Formula
Rearranging an equation to isolate a specific variable, often by using inverse operations.
- Apply inverse operations (addition/subtraction, multiplication/division, exponents/roots) to both sides.
- The order of operations is reversed when isolating a variable.
- Common in geometry, physics, and other applied math problems.
Memory trick: Unwrap the variable, inverse operations are your tools.