Answer:
-80π cm/s
(decreasing at a rate of 80π cm²/s)
Step-by-step explanation:
SA = area of Bases + area of the lateral surface
SA = 2πr² + 2πrh
using differential calculus
dSA/dt = 4πr dr/dt + 2π[ r dh/dt + h dr/dt]
= 4π(5cm)(-3cm/s) + 2π[ (5cm)(4cm/s) + (10cm)(-3cm/s)]
= -80π cm²/s or apprx. -251.33cm/s
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Answers & Comments
Answer:
-80π cm/s
(decreasing at a rate of 80π cm²/s)
Step-by-step explanation:
SA = area of Bases + area of the lateral surface
SA = 2πr² + 2πrh
using differential calculus
dSA/dt = 4πr dr/dt + 2π[ r dh/dt + h dr/dt]
= 4π(5cm)(-3cm/s) + 2π[ (5cm)(4cm/s) + (10cm)(-3cm/s)]
= -80π cm²/s or apprx. -251.33cm/s