Question

the rate of change of a area of circle w.r.t its radius r at r =6 cms is​

Answer 1

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Step-by-step explanation:

The area of a circle (A) with radius (r) is given by,

The area of a circle (A) with radius (r) is given by,A = πr2

The area of a circle (A) with radius (r) is given by,A = πr2Therefore, the rate of change of the area with respect to its radius r is

The area of a circle (A) with radius (r) is given by,A = πr2Therefore, the rate of change of the area with respect to its radius r isdAdr=ddr(πr2)=2πr

The area of a circle (A) with radius (r) is given by,A = πr2Therefore, the rate of change of the area with respect to its radius r isdAdr=ddr(πr2)=2πr∴When r = 6 cm,

The area of a circle (A) with radius (r) is given by,A = πr2Therefore, the rate of change of the area with respect to its radius r isdAdr=ddr(πr2)=2πr∴When r = 6 cm,dAdr=2π×6=12πcm2/s

Hence, the required rate of change of the area of a circle is 12π cm2/s.

Answer 2

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the rate of change of a area of circle w.r.t its radius r at r =6 cms is

$\huge{ \underline{\underline{\mathrm{ \red{Answer}}}}}$

The area of a circle (A) with radius (r) is given by,

$➺ \: \sf \: A = πr2$

Therefore, the rate of change of the area with respect to its radius r is

$➺ \: \sf \: dA/dr=d/dr(πr2)=2πr$

∴When r = 6 cm,

$➺ \: \sf \: dA/dr=2π×6=12π {cm}^{2} /s$

Hence, the required rate of change of the area of a circle is 12π cm2/s.