Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimeters of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15cm.

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimeters of gas per second. Find the rate at which the radius of the balloon increases when the radius is 15cm.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 9723 Points
20 days ago
In this question, the rate of pumping is given to us. Directly use formula for volume of sphere and find the rate of change of volume of sphere with respect to time(t) solve for rate of change of radius with respect to time(t). Complete step by step answer: Volume of sphere, V = 43πr3 Rate of change of volume V w.r.t to time(t)= dvdt=(dvdr)×(drdt)dvdt=43π×3r2×drdtdvdt=4πr2drdt Given, dvdt= Rate of pumping = 900cm3/sand r=15cm ⇒dvdt=4π×(152)(drdt)900=900π(drdt)(drdt)=900900π=1πcm/s Note- In order to solve such types of problems students must remember the formula for the volume of common geometrical shapes such as sphere. The major source of mistakes in such types of problems is due to the difference in the units given at different places, so students must take extra care of the units mentioned. Students should try to convert all the values in one common unit to avoid mistakes.

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free