Question

Relative error in the calculation of surface area of sphere is 0.12. Find the relative
error in the calculation of its volume.

Answer 1

We know that the formula of the surface area of the sphere = 4πR²

∴ Relative error in calculation of surface area = 2ΔR/R,

where ΔR is the error in Radius and R is the original Radius of the Sphere.

∴ 2ΔR/R = 0.12

∴ ΔR/R = 0.06 ------eq(i)

Now, Volume of the Sphere = 4/3 πR³

∴ Relative error in Calculation of Volume of Sphere = 3ΔR/R

= 3 × 0.06 (from eq(i))

= 0.18

Hence, relative error in calculation of volume is 0.18

Hope it helps.

Answer 2

Answer:

Given that, the relative error in calculation of surface area of sphere = 0.12.

Now, We know that, surface area of sphere = 4πr².

Hence, 2∆R/R = 0.12

So, ∆R/R = 0.12/2

∆R/R = 0.06

The Relative error in the radius of the sphere = 0.06.

Now, we know that the volume of sphere = 4/3 * πr³.

Hence, the relative error = 3∆R/R

Hence, = 3 * 0.06 = 0.18

Now, finding the percentage error of its volume = 0.18 * 100 = 18%