The Volume of a tin of radius r cm is given by V=pi*(40r-r^2-r^3). Find the positive value of r for which dV/dr=0 and find the value of V for this r.

Firstly differentiate the function V with respect to x (dV/dx)=pi*(40-2r-3r^2). Set dV/dr =0 and solve to find r. Divide both sides by pi and divide both side by -1 so that the r^2 term is positive (I personally find it easier to solve when the highest power coefficient is positive) (3r^2+2r-40=0). Factorise this expression ((3r-10)(r+4)=0). From this you can deduce the two values of x for which dV/dx=0 (r=10/3 and r =-4). Lastly substitute the positive value of r (10/3) into the expression for V (V=pi*(40-2(10/3)-3(10/3)^2)) = (2300*pi)/27.

CK
Answered by Chorley K. Maths tutor

4357 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I find the cartesian equation for a curve written in parametric form?


Curve D has equation 3x^2+2xy-2y^2+4=0 Find the equation of the tangent at point (2,4) and give your answer in the form ax+by+c=0, were a,b and c are integers.


f(x)=ln(3x+1), x>0 and g(x)=d/dx(f(x)), x>0, find expressions for f^-1 and g


The quadratic equation 2x^2+8x+1=0 has roots a and b. Write down the value of a+b and ab and a^2+b^2.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences