Browse by Stream
QnA
Home
Search for Exam, Articles, Questions
QnA
get app
Go To Your Study Dashboard
  1. Home
  2. Give answer! - Limit , continuity and differentiability - JEE Main-12
# Engineering

A spherical iron ball of rdius 10cm is coated with a layer of ice of uniform 

thickness that melts at a rate of  50 \: cm^{3}/min. When the thickness of 

the ice is 5 cm , then the rate at which the thickness ( in cm / min ) of the ice

decreases, is :

  • Option 1)

    \frac{1}{18\pi}

  • Option 2)

    \frac{1}{36\pi}

  • Option 3)

    \frac{5}{6\pi}

  • Option 4)

    \frac{1}{9\pi}

 

Answers (1)
P Plabita

Volume of ice , V=\frac{4}{3}\pi(R+x)^{3}-\frac{4}{3}\pi R^{3}

                         \frac{dV}{dt}=4\pi (R+x)^{2}\frac{dx}{dt}=50

                          \frac{dx}{dt}=\frac{50}{4\pi (R+x)^{2}}

                   at x = 5,

                         \frac{dx}{dt}=\frac{50}{4\pi (10+5)^{2}}=\frac{1}{18\pi}cm/min

So, option (1) is correct. 

                      


Option 1)

\frac{1}{18\pi}

Option 2)

\frac{1}{36\pi}

Option 3)

\frac{5}{6\pi}

Option 4)

\frac{1}{9\pi}

Similar Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 14999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
Start Now
 
Exams
Articles
Questions