Answer :
Sure, let's address John's solution step by step to identify his error and the correct approach.
Step 1:
John correctly sets up the formula for the central angle in radians:
[tex]\[ \text{Central angle (radians)} = \frac{\text{arc length}}{\text{radius}} \][/tex]
Step 2:
He correctly substitutes the given central angle and radius into the formula:
[tex]\[ 3\pi = \frac{\text{arc length}}{9} \][/tex]
Step 3:
Here, John should solve for the arc length. The correct operation to isolate the arc length is to multiply both sides by the radius (9):
[tex]\[ \text{arc length} = 3\pi \times 9 = 27\pi \][/tex]
Thus, the error John made was in step 3. He incorrectly divided instead of multiplying by the radius. Therefore, the correct statements are:
John made his first error in step 3. He divided instead of multiplying, but he should have multiplied by 9.
Step 1:
John correctly sets up the formula for the central angle in radians:
[tex]\[ \text{Central angle (radians)} = \frac{\text{arc length}}{\text{radius}} \][/tex]
Step 2:
He correctly substitutes the given central angle and radius into the formula:
[tex]\[ 3\pi = \frac{\text{arc length}}{9} \][/tex]
Step 3:
Here, John should solve for the arc length. The correct operation to isolate the arc length is to multiply both sides by the radius (9):
[tex]\[ \text{arc length} = 3\pi \times 9 = 27\pi \][/tex]
Thus, the error John made was in step 3. He incorrectly divided instead of multiplying by the radius. Therefore, the correct statements are:
John made his first error in step 3. He divided instead of multiplying, but he should have multiplied by 9.
