Class 12

Math

Calculus

Application of Derivatives

If the radius of a sphere is measured as 9 cm with an error of 0.03 cm, then find the approximate error in calculating its volume.

$δr$=0.03

we know,

$v=34 πr_{3}$

differentiate with respec to r

$δrδv =δrδ (34 πr_{3})$

$δv=4πr_{2}δr$

$δv=4(3.14)(9_{2})(0.03)$

$δv=30.520cm_{3}$