Question

what is percentage error in surface area of the sphere when error is measuring its radius is 2%

Answer 1

Hey mate ur answer in attachment........

Answer 2

Answer:

The percentage error in the surface area of the sphere is 4%.

Explanation:

The surface area of the sphere is given as,

$S=4\pi r^2$       (1)

Where,

S= surface area of the sphere

r=radius of the sphere

By using equation (1) the percentage error in surface area is given as,

$\frac{\Delta S}{S}=2\frac{\Delta r}{r}$                (2)

Where,

ΔS/S=percentage error in surface area

Δr/r=percentage error in radius

As per the question, the percentage error in radius is 2%. By substituting this in equation (2) we get;

$\frac{\Delta S}{S}=2\times 2\%=4\%$

Hence, the percentage error in the surface area of the sphere is 4%.