Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2015MathematicsApplication of Derivatives

A cone whose height is always equal to its diameter, is increasing in volume at the rate of 40 ~cm ^3 / s . At what rate is the radius increasing when its circular base area is 1 ~m ^2 ?

Options

  1. A1 ~mm / s
  2. B0.001 ~cm / s
  3. C2 ~mm / s
  4. D0.002 ~cm / s

Correct answer

D. 0.002 ~cm / s

Step-by-step solution

Let h be the height, r be the radius of the base and V be the volume of the cone at time t . Then, V= 1 3 r^2 h V= 2 3 r^3 [ h=2 , given ] On differentiating both sides w.r.t. t , we get d V d t =2 r^2 d r d t 40=2(10)^4 d r d t [ r^2=1 ~m ^2=10^4 ~cm ^2 . and d V d t =40 ~cm ^3 / s , given ] d r d t = 2 1000 ~cm / s =0.002 ~cm / s

Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

Consider the quadratic equation a x^2+b x+c=0 , where 2 a+3 b+6 c=0 and let g(x)= a x^3 3 + b x^2 2 +c x . Statement-I : The given quadratic equation ax ^2+ bx + c =0 has at least 2025The difference between the absolute maximum and absolute minimum values of the function f(x)=2 x^3-15 x^2+36 x-30 on [-1,4] is 2025If f(x)=x e^ x(1-x) , x R , then f(x) is 2025The angle between the curves y ^2= x and x ^2= y at the point (1,1) is 2025If the tangent of the curve 4 y^3=3 a x^2+x^3 drawn at the point (a, a) forms a triangle of area 25 24 sq.units with the coordinate axes then a = 2025If the function f(x)= x- ^2 x is defined on the interval [- , ] , then f is strictly increasing in the interval 2025If the Lagrange's mean value theorem is applied to the function f(x)=e^x defined on the interval [1,2] and the value of c (1,2) is k , then e^ k-1 = 2025If the tangent to the curve x y+a x+b y=0 at (1,1) makes an angle Tan ⁻¹ 2 with X -axis, then ab a + b = 2025 Full Application of Derivatives list All Manipal MET PYQs