Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT2024MathematicsApplication of DerivativesActual

The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is

Options

  1. A384 3
  2. B768 3
  3. C768 3
  4. D1152 3

Correct answer

B. 768 3

Step-by-step solution

12^2=r^2+ ( h 2 )^2 V= r^2 h V= (144- h^2 4 ) h V=144 h- 4 h^3 d V d h =144 - 3 4 h^2 d V d h =0 144 = 3 4 h^2 h^2=48 4 h=8 3 12^2=r^2+48 r^2=96 Volume = r^2 h= 96 8 3 =768 3 ~cm ^3 .

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 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 2023If f(x)= x, g(x)= 2 x, h(x)= 3 x and I(x)= x , then which of the following option is correct? 2023 Full Application of Derivatives list All BITSAT PYQs