Question

2 points
11. If the % error in the
measurement of a side of the
cube is 2%, then percentage
errors respectively inits
volume and area are - *
(a) 6%, 4%
(b) 4%, 6.5%
ОО
(c) 3%, 2%
Ol (d) 9%, 2%​

Answer 1

Answer:

(a) 6%, 4%

Explanation:

(a)% error in side of a cube = 2%

Δa/a*100 = 2%

Volume of cube

V = a³

⇒ΔV = 3a² Δa

Divide with Volume on both sides

⇒ΔV/V = 3a² Δa/V = 3a² Δa/a³    

             = 3 Δa/a

Multiply with 100 on both sides

⇒ ΔV/V *100 = 3 Δa/a * 100

∴ ΔV/V % = 3 Δa/a%

                = 3*2

                = 6%

(b) S = 6 a²

⇒ΔS = 6*2a Δa

Divide with S on both sides

⇒ΔS/S = 12a Δa/S = 12a Δa/6a²

            = 2 Δa/a

Multiply with 100 on both sides

∴ΔS/S% = 2 Δa/a%

             = 2*2

             = 4%