Question

प
कीजिए।
एक वृत्तीय प्लेट की त्रिज्या 2 सेमी है। गर्म करने पर
त्रज्या में प्रसार 0.02 सेमी/सेकण्ड की दर से होता है।
जब त्रिज्या 2.1 सेमी हो तो क्षेत्रफल प्रसार की दर ज्ञात
कीजिए।​

Answer 1

$\huge{\underline{\rm{\red{\bf{Given:-}}}}}$

Radius of the circular late = 2 cm

Rate expanding = $\sf \dfrac{dr}{dt} =0.02 \: cm/sec$

$\huge{\underline{\rm{\red{\bf{To \: Find:-}}}}}$

The rate of expansion of the area when the radius is 2.1 cm.

$\huge{\underline{\rm{\red{\bf{Solution:-}}}}}$

We know that,

• r = Radius
• d = Diameter
• dA = Derivative of acceleration
• dt = Derivative of time

Given that,

Radius of the circular late = 2 cm

Rate expanding = $\sf \dfrac{dr}{dt} =0.02 \: cm/sec$

$\boxed{\sf Area \ of \ circle= \pi r^{2}}$

On differentiating and we get,

$\longrightarrow \sf \dfrac{dA}{dt} = 2 \pi r \dfrac{dr}{dt}$

Substituting their values, we get

$\implies \sf \dfrac{dA}{dt} = 2 \pi \times 2.1 \times 0.02$

Multiplying them,

$\implies \sf \dfrac{dA}{dt} =0.084 \pi \: cm^{2}/sec$

Therefore, the rate of expansion of the area is $\sf \bf{0.084 \pi \: cm^{2}/sec}$

$\huge{\underline{\rm{\red{\bf{To \: Note:-}}}}}$

dA/dT denotes the rate of change of the available energy of the system per degree change in temperature.

The SI unit of jèrk is the meter per second cubed.

An alternate unit is the g per second.