Q.the radius r and area a of a circle are related by an equation a= pie r squared. write and euation the relates da/dt to dr/dt
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Area of circle = π²
using this relation we are required to find the relationship between (DA / DT ) and ( DR / DT)
━─━─━─━─◈─━─━─━─━
➛d/dx (a) = a¹ × da/dx
━─━─━─━─◈─━─━─━─━
chain differentation:
when we change it will
➛d/dt ( area ) = d/dt (πr²)
➛Da/DT = π × dr²/d²
➛Da/dt = π × 2r × dr/dt
━─━─━─━─◈─━─━─━─━
DA/DT = 2πr × Dr/Dt
━─━─━─━─◈─━─━─━─━
❑Hence this is the required relation❑
Explanation:
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