Question

the side of a cube is measured with a vernier calipers of least count 0.01 cm is 3.00 cm. the maximum possible error in the measurement of volume is
answer: + or - 0.27 cm3​

Answer 1

Given info : The side of a cube is measured with a vernier calipers of least count 0.01 cm is 3.00 cm.

To find : the maximum possible error in the measurement of volume is.

solution : volume of cube , V = a³ = (3cm)³ = 27 cm³

Here , V = a³

Differentiating both sides,

dV = 3a² da

Now dividing by V we get,

dV/V = 3a²da/V

⇒dV/V = 3a²da /a³

⇒dV/V = 3da/a

now let's consider dV = ∆V and da = ∆a

So, ∆V/V = 3 ∆a/a

Here V = 27 cm³, ∆a = 0.01 cm , a = 3cm

so, ∆V/27 = 3 × 0.01/3 = 0.01

⇒∆V = 0.27 cm³

Therefore the maximum error in the measurement of volume of cube is ±0.27 cm³