Question

A rectangular block of metal has mass (m) = (39.3+-0.1)gram, length l = (5.12+-0.01)cm, breadth b = (2.56+-0.01)cm and height h = (0.37+-0.01) cm. Find the percentage
error in the determination of density.​

Answer 1

this is similar solution as

Volume of cylinder , V = πr²L = π(d/2)²L = πd²L/4

Here, r is the radius of base of cylinder,

L is the length of cylinder ,

and d is diameter.

For finding error in volume, we have to use the formula,

∆V/V = 2∆d/d + ∆L/L

⇒∆V/V × 100 = 2 × {∆d/d × 100} + ∆L/L × 100

⇒ % error in volume = 200 × ∆d/d + 100 × ∆L/L

Here, ∆d = 0.01 , d = 1.6 , ∆L = 0.1 and L = 5

∴ % error in volume = 200 × 0.01/1.6 + 100 × 0.1/5

= 20/16 + 2

= 1.25 + 2

= 3.25 %

Hence, percentage error in volume is 3.25 %