Question

The height of a cylinder is equal to its radius. If an error of $1\%$ is made in its height. Then percentage error in its volume is

• A. $1$%
• B. $2$%
• C. $3$%
• D. $4$%

Answer 1

The correct option is C $3$%

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

$\frac{\Delta r}{r}=\frac{\Delta h}{h}=1\%=0.01$

$\frac{\Delta v}{v}=3\left(\frac{\Delta r}{r}\right)=3\times 1\%=3\%$

So ever in volume of the sphere due

do ever in measured value of r = 3%