If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at which the diameter decreases whe

Question

sergiy2304 [10]

2 years ago

10

If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at which the diameter decreases whe

n the diameter is 10 cm.

Mathematics

2 answers:

yanalaym [24] · Answer 1 · 2022-04-21T05:50:33+03:00

yanalaym [24]2 years ago

6 0

Dr/dt = -7 / (pi*r*8)

= -7 / pi*5*8

= - 0.56 cm/min

Hope this helps

vivado [14] · Answer 2 · 2022-04-21T03:30:07+03:00

vivado [14]2 years ago

3 0

Surface area: S
radius: r
diameter: e
time: t

[dS/dt] = [dS/de]*[de/dt] => de/dt = [dS/dt] / [dS/de]

S = 4pi*r^2 = 4p*i(e/2)^2 = pi*e^2 => dS/de =2pi*e

dS/dt = 7cm^2 / min

de / dt = [2pi*e] / [7cm^2/min] =[7cm^2/min] / [2pi*10cm] = 0.11 cm/min