hard differentiation

[craggy bolt]

Bit stuck on this question <@&791435371564892232>

[mystic viper]

Basically it says when t=3

Which means it’s 24 cm^3 full

dV/dh = dv/dt • dt/dh

Dv/dh= 3πh^2/12

At t=3 dv/dh=24

Rearrange for h

Then sub back in

[craggy bolt]

could u plz show it on a paper like i get wht to do but im just getting confused But stuck on this question <@&791435371564892232>

[timid cradle]

Do u get how to find the volume when t=3

[mystic viper]

Hold on

[craggy bolt]

ye

[mystic viper]

Volume is 24 mb not dv/dh

[timid cradle]

So sub in 24 to find h first

And then sub in that value of h into dv/dh

[mystic viper]

Then do some simplification from here

[craggy bolt]

but how do i show that to be 6(6pi)^1/3

like it said at the strt

@mystic viper

[mystic viper]

Factorise the highest cube number same as simplfying surds

[craggy bolt]

wait so i take 6^3 out the top

bit

?

@mystic viper im trying to do it but im not getting the final answer

[mystic viper]

Alright so

First simplify it by squaring it the 288

(82944pi)^1/3 / 64^1/3
(1296pi)^1/3

Then u can simplify that further

Just keep factoring out 6^3

And you’ll get there

[craggy bolt]

could u srry ik im being a pain but to do it on paper

@mystic viper sorry

[mystic viper]

Look
1296/6=216
216=6^3
Hence
(6^3(6pi))^1/3
6(6pi)^1/3

[craggy bolt]

in this step is the pi not on the outside

[mystic viper]

No

If you get show that answers

Once u get Ute final answer

Check with u calculator

If it matches just make it equal to that

[craggy bolt]

ye i get u

tysm