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C2 help, pic provided

The slant height of a cone is 18cm find the volume of the cone in terms of h, the perpendicular height from the base ....my working:
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Reply 1
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madfish
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I think my method is completely flawed

how should I do it? I am trying to work out the perpendicular height by Pythagoras theorem but it looks to messy
Reply 2
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joostan
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Original post by madfish
The slant height of a cone is 18cm find the volume of the cone in terms of h, the perpendicular height from the base ....my working:


You are trying to express the volume in terms of h.
Why have you expressed h in terms of r?
I'd suggest starting over.
Hint: r2 = 182 - h2
(edited 11 years ago)
Reply 3
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madfish
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Original post by joostan
You are trying to express the volume in terms of h. Why have you expressed h in terms of r?
I'd suggest starting over.
Hint: r2 = 182 - h2


okay so v= 324pir^2 - pir^2h^2 all over 3

how on earth to I differentiate that?
Reply 4
Avatar for joostan
joostan
13
Original post by madfish
okay so v= 324pir^2 - pir^2h^2 all over 3

how on earth to I differentiate that?


You've still got r's in the equation . . .
They need getting rid of, though you're pretty close :smile:
Reply 5
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madfish
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Original post by joostan
You've still got r's in the equation . . .
They need getting rid of, though you're pretty close :smile:


ehh I um sure of how to do the next part, would you mind helping?:colondollar:(I am self teaching) :/
Reply 6
Avatar for joostan
joostan
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Original post by madfish
ehh I um sure of how to do the next part, would you mind helping?:colondollar:(I am self teaching) :/


Just a little help, nothing too grand. . .

r2 = 182 -h2
Sub this in to 1/3 pi*r2h
Reply 7
Avatar for madfish
madfish
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Original post by joostan
Just a little help, nothing too grand. . .

r2 = 182 -h2
Sub this in to 1/3 pi*r2h


okay so v= 1/3 (324pih-pih^3) ?
Reply 8
Avatar for joostan
joostan
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Original post by madfish
okay so v= 1/3 (324pih-pih^3) ?


Correct though you could factor out pi*h if you were really keen :tongue:
Reply 9
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madfish
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Original post by joostan
Correct though you could factor out pi*h if you were really keen :tongue:


i just differentiated this to get 108pi -pih^2

correct?:P
Reply 10
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joostan
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Original post by madfish
i just differentiated this to get 108pi -pih^2

correct?:P


Yes
Reply 11
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madfish
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Original post by joostan
Yes


thanks man :smile: appreciated :smile:
Reply 12
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joostan
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Original post by madfish
thanks man :smile: appreciated :smile:


De nada

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