Question

Volume of a balloon. The volume V(in cubic meters) of a hot air balloon is given by v(r)=4/3πr^3. If the radius r is increasing with time t (in seconds) according to the formula r(t)= 2/3t^3, t≥0 find the volume V as a function of the time t.

Answer 1

I believe you replace r in v(r) with r(t). V(t)=4/3(pi)(2/3t^3)^3

Answer 2

Expand out (2/3t^3)^3 and simplify.

Answer 3

@iPwnBunnies , try asking for their ideas too. It will ensure that they are incorporated into learning the material, and they are more likely to remember it too.
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Answer 4

@whpalmer4 can you help?

Answer 5

What do you think you should do given the provided information?

Answer 6

I have no clue =(

Answer 7

so far i have (2/3)^3 t^9

Answer 8

Ok, so you want that in terms of t

Answer 9

ok...holy crud im horrible at this stuff.. explain how please =(

Answer 10

Alright. So you have r(t). In other words, the function of t. Your volume requires a radius or r. Since r is already defined, you must substitute r into the volume equation. Try it :)

Answer 11

@OrthodoxMan It's the algebra, I think

Answer 12

v(t)= 4/3π[(2/3)t^3]^3 = (2/3)^3 t^9 ?

Answer 13

You forgot the initial constant

Answer 14

Initial constant: 4/3 pi

Answer 15

v= 4/3 π (8/27 t^9)

Answer 16

now simplify so it isn't so ugly looking (get rid of as many fractions as you can)

Answer 17

32/81πr^9

Answer 18

That looks right to me.

Answer 19

YAY!!!! =) thanks you guys! I dont know who to award...you all helped so much...