Question

If the percentage error in radious of sphere is 2% , the percentage error in its volume is​

Answer 1

Answer

⇒Volume of sphere is given by,

$v = \frac{4}{3} \pi {r}^{3}$

⇒Where,

◇V= volume of the sphere

◇r=radius of the sphere.

⇒Of these, v and r are the only variables where others are constant. So, we can write,

$v \: \alpha \: {r}^{3}$

⇒Let's take

• %v/v = percentage error in volume
• %r/r = percentage error in radius

⇒then,

$\frac{\%v}{v} = 3 \times \frac{\%r}{r}$

⇒Substituting given values in the above equation, we get,

$\frac{\%v}{v} = 3 \times 2 \\ = 6\%$

hope it helps...!!!