Math Is Fun Forum

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

[ASK] Balloon Being Blown

Icha is going to blow a sphere-shaped rubber balloon. She uses a pump to infuse the air with the volume addition rate [MATH]40cm^3/s[/MATH]. If the radius addition rate is 20 cm/s, the radius of the sphere after being blown is ....
A.

cm
B.

cm
C.

cm
D.

cm
E.

cm

Please give me some hints. Thanks.

Last edited by Monox D. I-Fly (2018-03-17 13:59:38)

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Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: [ASK] Balloon Being Blown

hi Monox D. I-Fly

This is a type of calculus question.  You are told dV/dt the rate of change of volume, and dr/dt, the rate of change of radius.  So construct a chain rule type equation:

dV/dr = dV/dt times dt/dr

So you can calculate dV/dr.  But there's a formula for V in terms of r.  Differentiate it and set equal to the above and solve for r.

Note: dV/dr will change as r increases.  If dV/dt is constant then dr/dt is not.  So the given value (20) must be the rate of change at an instant and you will be calculating the radius at that time.

If the radius addition rate is 20 cm/s, the radius of the sphere after being blown is ....

So I would have worded this "When the radius is increasing at 20cm/s, what is the radius at this moment?"

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] Balloon Being Blown

?

---

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,140

Re: [ASK] Balloon Being Blown

Yes, that's what I think.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Monox D. I-Fly

Member

From: Indonesia

Registered: 2015-12-02

Posts: 2,000

Re: [ASK] Balloon Being Blown

Okay, thank you bob!

---

Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.