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KatRina [158]
1 year ago
13

Air is being pumped into a spherical balloon so that its volume increases at a rate of 150 cm3/s. How fast is the radius of the

balloon increasing when the diameter is 20 cm?.
Physics
1 answer:
Slav-nsk [51]1 year ago
3 0

0.119cm/s is the radius of the balloon increasing when the diameter is 20 cm.

<h3>How big is a circle's radius?</h3>

The radius of a circle is the distance a circle's center from any point along its circumference. Usually, "R" or "r" is used to indicate it.

A circle's diameter cuts through the center and extends from edge to edge, in contrast to a circle's radius, which extends from center to edge. Essentially, a circle is divided in half by its diameter.

dv/dt = 150cm³/s

d = 2r = 20cm

r = 10cm

find dr/dt

Given that the volume of a sphere is calculated using

v = 4/3πr³

Consider both sides of a derivative

d/dt(v) = d/dt( 4/3πr³)

dv/dt =  4/3π(3r²)dr/dt = 4πr²dr/dt

Hence,

dr/dt = 1/4πr².dv/dt

dr/dt = 1/4π×(10)²×150

dr/dt = 1/4π×100×150

dr/dt = 0.119cm/s.

To know more about radius visit:

brainly.com/question/15053236

#SPJ4

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