Question

The radius of the sphere is changing at the rate of 0.1cm/second.the rate of change of its surface area when the radius is 200cm.​

Answer 1

Hey Buddy

Here's The Answer

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We'll be using differentiation

Given :

• Radius ( r ) = 200 cm
• change w.r.t. is 0.1 cm/second OR d( r ) / dt = 0.1 cm/sec

To Find :

• Rate of change of surface area, when r = 200 OR d(A) / dt = ?

Notations :

• radius = r
• Area = a

• Surface area of sphere ( A )

=> A = 4 × π × r²

Differentiating w.r.t. time

=> d(A) / dt = 4 × π × 2 × r × d( r )/dt

=> d(A) / dt = 8 × π × r × d( r )/dt

Putting value of d( r )/dt

=> d(A) / dt = 8 × π × 0.1 × r

Putting value of r = 200

=> d(A) / dt = 8 × π × 0.1 × 200

=> d(A) / dt = 160π cm²/sec

So, the area will change at 160π cm²/sec

Hope It Helps.