Final answer:
To determine the possible error in the area of a circular template when the radius changes by 0.02, you calculate the derivative of the area formula and multiply by the radius error, resulting in a maximum possible error of approximately 1.3 cm² for a radius of 10cm.
Step-by-step explanation:
The question asks to determine the possible error in calculating the area of a circular template with a given change in its radius. The area of a circle is given by the formula A = πr², where 'A' is the area and 'r' is the radius. If the radius has a possible error, this would affect the calculated area of the circle. Since the radius error is given as 0.02, and the exact radius is 10cm, the maximum error in the area can be found by taking the derivative of the area with respect to the radius 'r' and then multiplying by the error in the radius (0.02).
First, calculate the derivative of the area with respect to the radius, which is 2πr. Multiply this by the radius error of 0.02 to find the maximum error in the area. For r = 10cm, this would be 2π(10cm)(0.02) = 1.25664 cm². However, since the original radius is given to two significant figures, the calculated error should also be presented to two significant figures, resulting in 1.3 cm².
Thus, the maximum possible error in calculating the area of the template is approximately 1.3 cm².