Question

The diameter of a cylinder is(1.6±0.01)cm and its length is (5.0±0.1)cm . Calculate percentage error in its volume.

class11th
Errors and measurements

Answer 1

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 %

Answer 2

Answer:

Explanation:

The simple explanation is given below Hope it helps!!