The diameter and altitude of a right circular cone, at a certain instant, were found to be 10   cm and 20   cm respectively. If its diameter is increasing at a rate of 2   cm / s , then at what rate must its altitude change, in order to keep its volume constant?

Question

The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 &#160; cm and 20 &#160; cm respectively. If its diameter is increasing at a rate of 2 &#160; cm / s , then at what rate must its altitude change, in order to keep its volume constant?

Aicharya · Accepted Answer

Let D is diameter, h is altitude and r is radius of the right circular cone. d D d t = 2 cm / s d r d t = 1 cm / s V = 1 3 &#960; r 2 h d V d t = 1 3 &#960; d r 2 h d t d V d t = 1 3 &#960; r 2 d h d t + 2 r d r d t &#215; h 0 = &#960; 3 25 d h d t + 10 &#215; 20 &#215; 1 0 = 25 d h d t + 200 d h d t = - 8 cm / s .

The diameter and altitude of a right circular cone, at a certain instant, were found to be 10   cm and…

Solution

The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 &#160; cm and…

Solution

The diameter and altitude of a right circular cone, at a certain instant, were found to be 10 cm and…