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Question 12 - 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 12 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.Given Radius of sphere = r = 9 cm Error in radius = ∆r = 0.03 cm We need to find Error in calculating Volume Let Volume of sphere = V = 𝟒/𝟑 𝝅𝒓^𝟑 ∴ We need to find ∆V Now, ∆V = 𝑑𝑉/𝑑𝑟 ∆r = 𝑑(4/3 𝜋𝑟^3 )/𝑑𝑟 ∆r = 4/3 𝜋 (𝑑𝑟^3)/𝑑𝑟 ∆r = 4/3 𝜋 (3𝑟^2 )(0.03 ) = 4𝜋𝑟^2(0.03) = 4𝜋(9)2 (0.03) = 9.72𝝅 cm3 Hence, approximate error in calculating volume is 9.72𝜋 cm3
