Question:medium
If a circular plate is heated uniformly, its area expands $3c$ times as fast as its radius, then the value of $c$ when the radius is $6$ units, is
If a circular plate is heated uniformly, its area expands $3c$ times as fast as its radius, then the value of $c$ when the radius is $6$ units, is
Show Hint
In rate problems, always:
1. Write the formula first
2. Differentiate with respect to time
3. Substitute the given rate relation
4. Solve systematically
Updated On: May 8, 2026
- \( 4\pi \)
- \( 2\pi \)
- \( 6\pi \)
- \( 3\pi \)
- \( 8\pi \)
Show Solution
The Correct Option is A
Solution and Explanation
Was this answer helpful?
0
Top Questions on Rate of Change of Quantities
- The diagonal of a square is changing at the rate of \( 0.5 \, \text{cm/sec} \). Then the rate of change of area, when the area is 400 \( \text{cm}^2 \), is equal to:
- BITSAT - 2012
- Mathematics
- Rate of Change of Quantities
- The cost of running a bus from $A$ to $B$ , is $Rs.\left(av+\frac{b}{v}\right)$ where $v$ km/h is the average speed of the bus. When the bus travels at $30\, km/h$, the cost comes out to be $Rs.\, 75$ while at $40\, km/h$, it is $Rs. \,65$. Then the most economical speed (in $km/ h$) of the bus is :
- JEE Main - 2013
- Mathematics
- Rate of Change of Quantities
- If $f(x)=(ax+b)sin~x+(cx+d)cos~x$, then the values of a, b, c and d such that $f^\prime(x)=x~cos~x$ for all x, are
- MET - 2010
- Mathematics
- Rate of Change of Quantities
- The radius of a cylinder is increasing at \(2\,m/s\) and height is decreasing at \(3\,m/s\). When \(r=3\,m, h=5\,m\), rate of change of volume is:
- MET - 2020
- Mathematics
- Rate of Change of Quantities
- Want to practice more? Try solving extra ecology questions todayView All Questions
