The radius of a sphere is measured to be 2.1 plus minus 0.5 cm calculate surface area with error limits and its volume percentage
Answers
Given :
The radius of sphere measured = ( 2.1 0.5 ) cm
To Find :
The surface area of sphere with error limits
The volume percentage of sphere
Solution :
∵ Radius of sphere measured = ( 2.1 0.5 ) cm
∵ Surface area of sphere = A = 4 × π × radius²
= 4 × 3.14 × (2.1 cm)²
= 55.4 cm²
Now,
= 2 ×
i.e = 2 ×
Or, ΔA = 2 × A ×
Or, ΔA = 2 × 55.4 cm² ×
∴ ΔA = 26.3 cm²
Change in surface Area = ΔA = 56.4 cm²
Surface Area with error limit = ( 55.4 26.3 ) cm²
Again
∵ Volume of sphere = × π × radius³
= × 3.14 × ( 2.1 cm)³
= 38.77 cm³
Now,
= 3 ×
i.e = 3 × ( )²
Or, ΔV = 3 × V × ( )²
Or, ΔV = 3 × 38.77 cm³ × ( )²
∴ ΔV = 128.23 cm³
Change in volume = ΔV = 128.23 cm³
Volume with error limit = ( 38.77 128.23 ) cm³