The radius of a circle is given as 2.8cm to 2significant figures(a)if c is the circumference of the circle, determine the limits between which c/π lies (b) by takingπ to be 3.142, find, to4significant figures the line between which the circumference lies
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.