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Question 7 - Finding approximate value- Statement questions - Chapter 6 Class 12 Application of Derivatives
Last updated at April 16, 2024 by Teachoo
Finding approximate value- Statement questions
Chapter 6 Class 12 Application of Derivatives
Concept wise
- Finding rate of change
- To show increasing/decreasing in whole domain
- To show increasing/decreasing in intervals
- Find intervals of increasing/decreasing
- Finding slope of tangent/normal
- Finding point when tangent is parallel/ perpendicular
- Finding equation of tangent/normal when point and curve is given
- Finding equation of tangent/normal when slope and curve are given
- Finding approximate value of numbers
- Finding approximate value of function
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Finding approximate value- Statement questions
- Finding minimum and maximum values from graph
- Local maxima and minima
- Minima/ maxima (statement questions) - Number questions
- Minima/ maxima (statement questions) - Geometry questions
- Absolute minima/maxima
Transcript
Question 7 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.Let r be the radius of the sphere Given r = 9 m Error in measurement of radius = ∆𝑟 ∆𝑟 = 0.03 m Surface area of the sphere = S = 4𝜋𝑟^2 We need to find the error in calculating the surface area ∆ S ∆ S = 𝑑𝑠/𝑑𝑟×∆"r" = (𝑑("4" 𝜋𝑟^2))/𝑑𝑟×∆"r" = "4" 𝜋 (𝑑(𝑟^2))/𝑑𝑟×∆"r" = 8𝜋r × 0.03 = 8𝜋(9) (0.03) = 2.16𝜋 hence the approximate error is 2.16𝝅 m2
