The radius of circular disk is 18cm with a maximum error of 0.2cm. Estimate the

maximum error in calculated area of the disk.

b) The circumference of a sphere was measured to be 64cm with a maximum error of 0.5.

Estimate the maximum error in the calculated surface area of the sphere.

(Volume and Surface area of a sphere of radius r: ! = !

!!!, ! = 4!!!. )

!

let r be radius ,x be the diameter of the sphere

x=40

To estimate the maximum error in the calculated area of the disk, we can use the formula for the area of a circle:

A = πr^2

where A is the area and r is the radius. Taking the derivative of this formula with respect to r, we get:

dA/dr = 2πr

This derivative represents the rate at which the area changes with respect to the radius. We can use this rate to estimate the change in the area when the radius changes by a small amount.

Given that the radius has a maximum error of 0.2 cm, we can use this value to calculate the maximum error in the area. Using the formula for the error propagation of a function with one variable and rounding to the appropriate number of decimal places, we can estimate the maximum error in the area of the disk as follows:

Maximum error in area = |dA/dr| * maximum error in radius
= |2πr| * maximum error in radius
= 2π * 18 * 0.2
= 7.2π
≈ 22.62 cm^2

Therefore, the maximum error in the calculated area of the disk is approximately 22.62 cm^2.