This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to problems 3 and 4: 3. Calculate the perimeter of a circle. To calculate a specific numerical perimeter (circumference) of a circle, the radius or diameter must be known. Without this information, we can only provide the general formula using the given value of . Step 1: State the formula for the circumference of a circle. The circumference C of a circle can be calculated using the radius r or the diameter d: C = 2 r or C = d Step 2: Substitute the given value of . The problem specifies using = 3(1)/(7). Converting the mixed number to an improper fraction: = 3(1)/(7) = ((3 × 7) + 1)/(7) = (21 + 1)/(7) = (22)/(7) Step 3: Provide the general formula with the specified . Substituting = (22)/(7) into the formulas: C = 2 × (22)/(7) × r = (44)/(7) r or C = (22)/(7) d Since no specific radius or diameter is provided, the perimeter cannot be calculated as a numerical value. 4. Calculate the circumference of a circle with the following radii or diameters: We will use = (22)/(7) for all calculations. a) r = 14 cm Step 1: Use the formula for circumference with radius. C = 2 r Step 2: Substitute the values for and r. C = 2 × (22)/(7) × 14 cm Step 3: Simplify the expression. C = 2 × 22 × (14)/(7) cm C = 2 × 22 × 2 cm C = 88 cm The circumference is 88 cm. b) r = 4 cm Step 1: Use the formula for circumference with radius. C = 2 r Step 2: Substitute the values for and r. C = 2 × (22)/(7) × 4 cm Step 3: Simplify the expression. C = (44)/(7) × 4 cm C = (176)/(7) cm The circumference is (176)/(7) cm. c) d = 21 cm Step 1: Use the formula for circumference with diameter. C = d Step 2: Substitute the values for and d. C = (22)/(7) × 21 cm Step 3: Simplify the expression. C = 22 × (21)/(7) cm C = 22 × 3 cm C = 66 cm The circumference is 66 cm. d) d = 7 cm Step 1: Use the formula for circumference with diameter. C = d Step 2: Substitute the values for and d. C = (22)/(7) × 7 cm Step 3: Simplify the expression. C = 22 cm The circumference is 22 cm. That's 2 down. 3 left today — send the next one.