Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A spherical iron ball of  radius is coated with a layer of ice of uniform thickness that melts at a rate of <img alt="50cm^{3}/min" src="https://learn.careers360.com/

A spherical iron ball of 10cm radius is coated with a layer of ice of uniform thickness that melts at a rate of 50cm^{3}/min. When the thickness of ice is 5cm, then the rate (in cm / min.) at which of the thickness of ice decreases, is :  
Option: 1 5/6\pi
Option: 2 1/54\pi
Option: 3 1/36\pi
Option: 4 1/18\pi
 

Answers (1)

best_answer

 

 

Derivative as Rate Measure -

Derivative as Rate Measure

We have seen that for quantities that are changing over time, the rates at which these quantities change are given by derivatives. If two related quantities are changing over time, the rates at which the quantities change are related. For example, if a balloon is being filled with air, both the radius of the balloon and the volume of the balloon are increasing. 

If a variable quantity y depends on and varies with a quantity x, then the rate of change of y with respect to x is  \frac{dy}{dx}.

A rate of change with respect to time is simply called the rate of change.

For example, the rate of change of displacement (s) of an object w.r.t. time is velocity (v). \mathit{v=\frac{ds}{dt}}

When limit  Δt? 0 is applied, the rate of change becomes instantaneous and we get the rate of change of displacement (s)  w.r.t. time at an instant.

\text{i.e. }\lim _{\Delta t \rightarrow 0} \mathit{\frac{\Delta s}{\Delta t}=\frac{d s}{d t}}

-

{V=\frac{4}{3} \pi(10+a)^{3}} \\ {\frac{\partial V}{\partial t}=4 \pi(10+a)^{2} \cdot \frac{\partial a}{\partial t}=50 \frac{c m^{3}}{\min }} \\ {4 \pi(10+5)^{2} \cdot \frac{\partial a}{\partial t}=50 \frac{c m^{3}}{\min }} \\ {\frac{\partial a}{\partial t}=\frac{1}{18 \pi} \frac{c m}{\min }}

Posted by

avinash.dongre

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: Hardwired to excel? Know BTech electrical engineering cut-offs at NITs
anam-khan

JEE Main 2025 chemistry needs conceptual understanding; 5 tips to score high
anam-khan

JEE Main 2025 exam city intimation slip for session 1 soon; paper pattern, exams from January 22

Latest Question