# physics

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The radius of sphere at therate of 4cm per second .at what ratis its surface area chang when theradius is 6cm

• physics -

You seem to have left out some words in your question, such as:

The radius of sphere IS INCREASING at the rate of 4cm per second.

Surface area is
A= 4*pi*R^2

The rate of increase of surface area is
dA/dt = 8*pi*R*(dR/dt)

Plug in 6 cm for R, and dR/dt = 4 cm/s, and compute

• physics -

R=4t (cm)
6=4t
t=1.5 s.
A=4πR²=4π(4t)²=
=64πt²=64π(1.5)²=452.4 cm²

• physics -

dA/dt = 64πt²=128 πt=128 π•1.5=603.2 cm²/s

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