Question

Calculate percentage error in area of a if have 12% error in its volume

Answer 1

Answer:

Percentage Error of Area = 8%

Explanation:

Volume = A³

= A × A × A

Let V = V + ∆V where V is the volume

∆V/V = 3∆A/A

Given that,

∆V/V × 100 (percentage error) = 12%

Substituting the value, we get

∆V/V × 100 = 3∆A/A × 100

12 = 3∆A/A × 100

=> ∆A/A × 100 = 12/3 = 4%

Area = A²

= A × A

Let P = P + ∆P where P is the area

∆P/P = 2∆A/A

=> ∆P/P × 100 = 2∆A/A × 100

∆P/P × 100 = 2 ( 4 ). [ ∆A/A × 100 = 4 ]

=> ∆P/P × 100 ( percentage error ) = 8%