Question

Helen draws a random circle.

She then measures its diameter and circumference.
She gets a circumference, C, of 405 mm correct to 3 significant figures
She gets a diameter, d, of 130 mm correct to 2 significant figures.
Helen wants to find the value of using the formula π =
= 응
Calculate the lower bound and upper bound for Helen's value of t.
Give your answers correct to 3 decimal places.

Answer 1

To find the lower and upper bounds for Helen's value of π, we can rearrange the formula for the circumference of a circle and substitute the given values. The lower bound is 3.116 and the upper bound is 3.116.

Step-by-step explanation:

To find the lower bound and upper bound for Helen's value of t, we can start by rearranging the formula for the circumference of a circle:

C = πd

Substituting the given values, we have:

405 mm = π * 130 mm

To find the lower bound, we can assume the value of π that gives the smallest possible circumference using the given diameter. This would be:

π = C/d = 405 mm / 130 mm = 3.1154...

To find the upper bound, we can assume the value of π that gives the largest possible circumference using the given diameter. This would be:

π = C/d = 405 mm / 130 mm = 3.1154...

Therefore, the lower bound for Helen's value of π is 3.116 and the upper bound is 3.116.