Question

If the ratio of the base radius and height of a cone is $1:2$ and percentage error in the radius is $k$ then percentage error in volume is

• A. $k$
• B. $2k$
• C. $3k$
• D. $4k$

Answer 1

The correct option is C $3k$

Given that the radius is half then the height of the cone so

Let $h=2r$(where r is radius and h is height of the cone)

volume of the cone$=v$

$=\left(\frac{1}{3}\right)\times \pi r^2\times h$

$=\left(\frac{2}{3}\right)\times \pi r^3$(because $h=2r$)

$\Delta v=\left(\frac{2}{3}\right)\pi \times 3r^2\Delta r$

$\Delta v=2\pi r^2\Delta r$

so finally,

$\left(\frac{\Delta v}{v}\right)\times 100=3\cdot \left(\frac{\Delta r}{r}\right)\times 100$

$=3\times k$.