alleryFind the rate at which the surface area of a balloon (sphere) is changing when radius is 10 cm and dr/dt = 0.1 cm/s:
A2π cm²/s
B4π cm²/s
C8π cm²/s (dS/dt = 8πr × dr/dt)
D16π cm²/s
Answer & Solution
Correct answer: C. 8π cm²/s (dS/dt = 8πr × dr/dt)
S = 4πr².
We have dS/dt = 8πr × dr/dt.
That is dS/dt = 8π × 10 × 0.1.
So dS/dt = 8π cm²/s ≈ 25.1 cm²/s.
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