If the radius of a sphere is measured as 7 m with an error of 0.0 | Filo

Class 12

Math

Calculus

Application of Derivatives

598
150

If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.

Solution: Solution:

\displaystyle{\left({v}+\angle{v}\right)}={v}+{v}'\angle<{l}{a}{t}{e}{x}>eqn(1)
\displaystyle\frac{<}{{l}}{a}{t}{e}{x}>{\left({v}-\angle{v}\right)}={v}-{v}'\angle{r}<{l}{a}{t}{e}{x}>eqn(2)
\displaystyle\frac{<}{{l}}{a}{t}{e}{x}>{2}\angle{v}={2}{v}'\angle<{l}{a}{t}{e}{x}>
\displaystyle\frac{<}{{l}}{a}{t}{e}{x}\ge\frac{{4}}{{3}}\pi\cdot{3}\cdot{49}\cdot{0.02}<{l}{a}{t}{e}{x}>
\displaystyle\frac{<}{{l}}{a}{t}{e}{x}\ge{8}\cdot{10}^{{-{{2}}}}\cdot{49}\cdot\pi<{l}{a}{t}{e}{x}>
\displaystyle\frac{<}{{l}}{a}{t}{e}{x}\ge{3.92}\pi{m}^{{3}}