A solid is formed by a cylinder of radius r and height h together with two hemisphere of radius r - Maths - Application of Derivatives

Question

A solid is formed by a cylinder of radius r and height h together
with two hemisphere of radius r at each end if the volume of the
solid is constant but radius r is increasing at the rate of 1/2pie
meter/ minute how fast mast h (height )be changing when r and h are
10 metres

Anuradha Sharma · Accepted Answer

Volume of the whole set up = πr2h+43πr3V =  πr2h+43πr3Differentiating with respect to 't' ,we get0 = 2πrhdrdt+πr2dhdt+4 πr2drdtGiven drdt= 1/2π, h = 10=r2π×10×10×12π+100π×dhdt+400π×12π=0dhdt= 3 π m/minute

A solid is formed by a cylinder of radius r and height h together with two hemisphere of radius r at each end. if the volume of the solid is constant but radius r is increasing at the rate of 1/2pie meter/ minute how fast mast h (height )be changing when r and h are 10 metres