Question

If the radius of a sphere is measured as 9 m with an error of 0.03 m. then find the approximate error in calculating its surface area.

Solution

Let r be the radius of the sphere and ∆r be the error in measuring the radius.
∴ r = 9 m, ∆r = 0.03 m. Let S be the surface area of sphere.
$therefore space space space space space straight S space equals space 4 πr squared Now comma space space space space space dS space equals space open parentheses dS over dr close parentheses increment straight r space equals space left parenthesis 8 πr right parenthesis space increment straight r space space space space space space space space space space space space space space space space space space space space space equals space 8 straight pi space cross times 9 space cross times space 0.03 space equals space 2.16 space straight pi space straight m squared therefore space space space space approximate space error space in space calculating space the space surface space area space equals 2.16 space straight pi space straight m squared$

For Daily Free Study Material Join wiredfaculty

Application Of Derivatives

If the radius of a sphere is measured as 9 m with an error of 0.03 m. then find the approximate error in calculating its surface area.

Some More Questions From Application of Derivatives Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location