Question

The radius of a sphere is 5.3+-0.1cm.calculate its surface area with error limits?

Answer 1

1 Answer

volume is  
V = 4/3 pi r^3

for r=5.3 we get that 

V = 4/3 * 3.1416 * 5.3^3 = 

623.6145 cm^3

for r= 5.3 - 0.1 = 5.2

V0 = 4/3 * 3.1416 * 5.2^3 = 588.9774 cm^3

and for r= 

5.3 + 0.1 = 5.4

V1 = 4/3 * 

3.1416 * 5.4^3 = 659.5837 cm^3

Then the percentage error for surface area 

is 

(V-V0)/V = 

(623.6145-588.9774)/623.6145 * 100 = 5.5542 % 
(V1-V)/V =  
(659.5837-623.6145)/623.6145 * 100 = 5.7679 %

percentage 

error in volume is in the interval [-5.5542%, 5.7679%]