The radius of circle is given as 2.8 cm to 2 significant figure
(a) If C is the circumference of the circle, determine the limits between which C/π lies.
(b) By taking π be 3.14; find to 4 significant figures the line between which the circumference lies
To solve the given problem, we can use basic formulas related to circles. Let's proceed step by step:
(a) To find the limits between which C/π lies, we need to calculate the smallest and largest possible circumference.
1. Calculate the smallest possible circumference:
By using the lower limit of the radius, we have:
C_min = 2πr_min,
where r_min = 2.8 cm (given lower limit).
Substituting the values:
C_min = 2π(2.8) cm.
2. Calculate the largest possible circumference:
By using the upper limit of the radius, we have:
C_max = 2πr_max,
where r_max = 2.8 cm (given upper limit).
Substituting the values:
C_max = 2π(2.8) cm.
Therefore, C/π can range between C_min/π and C_max/π.
(b) To find the limits between which the circumference lies when taking π as 3.14, we need to calculate the smallest and largest possible circumference.
1. Calculate the smallest possible circumference:
By using the lower limit of the radius, we have:
C_min = 2πr_min,
where r_min = 2.8 cm (given lower limit).
Substituting the values:
C_min = 2(3.14)(2.8) cm.
2. Calculate the largest possible circumference:
By using the upper limit of the radius, we have:
C_max = 2πr_max,
where r_max = 2.8 cm (given upper limit).
Substituting the values:
C_max = 2(3.14)(2.8) cm.
Therefore, the circumference can range between C_min and C_max when taking π as 3.14, to 4 significant figures.