Question

the percentage error in the measurements of radius of a disc is 2% . Maximum percentage error in the surface area of the disc will be​

Answer 1

Answer:

4%

Explanation:

radius % = 2%

Formula for area of circle = πr²

Area % = 2 * (r%)

            = 2 * 2

            = 4 %

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Answer 2

Given:

• The error in the radius of the sphere = 2%

To Find:

• The maximum percentage error in the surface area.

Solution:

We know the formula to find the surface area of the sphere. That is,

A = 4π$r^2$ → {equation 1}

We have Δr = 2%

So, ΔA = 4πΔ$r^2$ → {equation 2}

On dividing equation 2 by 1 we get,

⇒ ΔA/A = 2Δr/r

Substitute the values in the above formula.

⇒ ΔA/A = (2×2)/1000 = 4/1000 {multiplying the terms in the bracket and dividing them}

⇒ ΔA/A = 0.04

To get the error in terms of percentage we multiply the value by 100

⇒ 0.04×100 = 4%

∴ The maximum percentage error in the surface area = 4%