Second,
(Take it = 3.14.)
the side of a square sheet of metal is increasing at 3 centimetres per
minute. At what rate is the area increasing when the side is 10 cm long?
5. The radius of a circular soap bubble is increasing at the rate of 0.2 cm/s. Find
the rate of increase of its surface area when the radius is 7cm.
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The radius of a soap bubble is increasing at the rate of 0.2 cm/sec. At what rate the surface area of a bubble increasing when the radius is 7 cm and at what rate the volume of a bubble increasing when the radius is 5 cm ?
December 26, 2019avatar
Pari Yumnam
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ANSWER
Bubble is spherical.
(I)⇒ surface area =4πr
2
=5
Rate of change is given by :
dt
ds
=4π(2r)
dt
dr
at r=7cm
dt
dr
=0.2cm/se
dt
ds
=8×
7
22
×7×0.2
=8×22×
10
2
=
10
352
=35.2cm
2
/sec.
(II)Volume=v=
3
4
πr
3
Rate of change is :
dt
du
=
3
4
π(3r
2
)
dt
dr
=4πr
2
(
dt
dr
)
at r=5cm,
dt
dr
=0.2cm/sec
⇒
dt
dr
=4×
7
22
×25×0.2
=62.857cm
3
/sec.
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