Question

A right circular cylinder has radius r=10 cm. and height =20 cm. Suppose that the radius of

the cylinder is increased from 10 cm to 10.1 cm and the height does not change. Estimate the change in the velume of the cylinder. Also calculate the relative error and percentage error​

Answer 1

Answer:

Change in Vol = 126.3 cm^3

%ge error = 2 %

Step-by-step explanation:

Vol (V1) = π * 10*10*20 = 6283.18 cm^3

Vol(V2) = π*10.1*10*1*20 = 6409.48 cm^3

Change in Vol = V2-V1 = 126.3 cm^3... Answer

%ge Error = [(V2-V1)/V1] * 100 = 2%... Answer

Answer 2

Given,

Radius(r1) = 10cm

Height(h) = 20cm

New Radius(r2)= 10.1

To Find,

The change in the velume of the cylinder =?

The relative error =?

The percentage error​ =?

Solution,

From the formula of the cylinder,

Volume of the cylinder(v1) = π(r1)²h

Volume of the cylinder(v1) = π * 10² * 20

Volume of the cylinder(v1) = 2000π cm³

Similarly, new volume (v2) = π*(10.1)² *20

New volume of the cylinder (v2) = 2040.2π cm³

The change in the velume of the cylinder =  v2 - v1 = 2040.2π - 2000π

The change in the velume of the cylinder = 40.2π cm³

Relative error = v2 - v1 = 2040.2π - 2000π

Relative error = 40.2π cm³ = 126.2 cm³

Percentage error = 100 * (v2 - v1) / v1

Percentage error = 100 * (40.2π ) / 2000π

Percentage error = 40.2 / 20

Percentage error = 2.01%

Percentage error = 2%

Hence, the relative error is 40.2π and the percentage error is 2%.