Question

the error in the measurement of volume of a cube is 9 % find out error in measurement of area​

Answer 1

Answer:

6 %

Explanation:

error in volume =9%, so error in its edge is ,

a³= 9 %

3 a =9

a=9/3

a=3%

now surface area of cube is 6a²

then error will be 2 a =2*3 ( a=3)

P.S - neglect the constant 6 in 6a²

Answer 2

Concept:

• This question uses relative error calculations
• The relative error is the ratio of the difference between the expected and actual value to the actual value
• when x = a^t, relative error Δx/x = t (Δa/a)

Given:

• error in measurement of volume of cube  Δv/v= 9% = 0.09

Find:

• error in measurement of area

Solution:

• The volume of cube v = s^3 where s is the length of the cube
• Therefore, Δv/v = 3 Δs/s
• Δv/v = 9% = 3Δs/s
• Δs/s = 1/3(Δv/v ) = 3%
• The area of a cube A = 6s^2
• Error in measurement of area ΔA/A = 2Δs/s
• Therefore, ΔA/A= 2* 3% = 6%

The error in measurement of the area is 6%.

#SPJ2