Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2021MathematicsApplication of DerivativesActual

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

Options

  1. A2.46 cm ³
  2. B8.62 cm ³
  3. C9.72 cm ³
  4. D7.6 cm ³

Correct answer

C. 9.72 cm ³

Step-by-step solution

Let r be the radius of the sphere and r be the error in measuring the radius. Then, r=9 ~cm and r=0.03 ~cm Let V be the volume of the sphere. Then, array l V = 4 3 r³ dV dr =4 r² ( dV dr )_ r=9 =4 9²=324 array Let V be the error in V due to error r in r . Then, array l V = dV dr r V =324 0.03=9.72 cm ³ array

Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

The maximum area of rectangle inscribed in a circle of diameter R is 2024Consider the function f(x)= |x-1| x^2 , then f(x) is 2024The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is 2024If the angle made by the tangent at the point (x₀, y₀ ) on the curve x=12(t+ t t), y=12(1+ t)^2, 0 t 2 , with the positive x -axis is 3 , then y₀ is equal to 2024The altitude of a cone is 20 cm and its semivertical angle is 30^ . If the semi-vertical angle is increasing at the rate of 2^ per second, then the radius of the base is increasing 2024The point of inflexion for the curve y=(x-a)^n , where n is odd integer and n 3 is 2024The population p(t) at time t of a certain mouse species satisfies the differential equation d p(t) d t =0.5 p ( t )-450 . If p(0)=850 , then the time at which the population becom 2024The function f(x)= (1+x)- 2 x 2+x is increasing on 2023 Full Application of Derivatives list All BITSAT PYQs