Question

The measure of the diameter of
the cylinder is (1.60 + 0.01) cm and its
length is (5.0 + 0.1) cm. Calculate the
percentage error in its volume. ​

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 %

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