To answer part (a), we need to determine the range between which the value of c/π lies, given that the radius of the circle is given as 2.8 cm to 2 significant figures.
The circumference of a circle can be calculated using the formula C = 2πr, where C represents the circumference, π is a mathematical constant (approximately 3.14159), and r is the radius of the circle.
To find the lower limit of c/π, we can substitute the minimum value for the radius into the formula. Since the radius is given as 2.8 cm to 2 significant figures, the minimum value of the radius would be 2.75 cm (when rounded to two decimal places). Therefore, we can calculate the lower limit as follows:
Lower Limit = 2π(2.75)
Similarly, to find the upper limit of c/π, we can substitute the maximum value for the radius into the formula. Since the radius is given as 2.8 cm to 2 significant figures, the maximum value of the radius would be 2.85 cm (when rounded to two decimal places). Therefore, we can calculate the upper limit as follows:
Upper Limit = 2π(2.85)
To answer part (b), we need to find the range within which the circumference lies by taking π to be 3.142 and rounding the result to 4 significant figures.
Using the value of π as 3.142, we can write the circumference formula as C = 2(3.142)r. To find the range, we need to calculate the minimum and maximum values for the circumference.
For the lower limit, substitute the minimum radius value (2.8 cm) into the formula:
Lower Limit = 2(3.142)(2.8)
For the upper limit, substitute the maximum radius value (2.8 cm) into the formula:
Upper Limit = 2(3.142)(2.8)
Calculate the lower and upper limits and round the results to 4 significant figures to find the range within which the circumference lies.
Note: It's important to mention that the limits are not the exact values for the circumference; rather, they represent the range within which the circumference falls, considering the given radius and the approximation of π.