Home » Ask & Discuss » Mathematics. » Differential Calculus « Back to Discussion

Differential Calculus

Hot goIITian

Joined:	18 Jan 2009
Post:	193

24 Mar 2009 02:32:47 IST

0 People liked this

353

Passage - Functions

None

A cylinder is inscribed in a sphere of radius R. The volume V of the cylinder is written as V=f(x), where x is the height of the cylinder.

After this four questions are given that follow this passage. I'm giving one of them:-

If ${x}_{1}$ in the dom f is such that f( ${x}_{1}$ )= $\frac{\pi{{x}_{1}}^{2}}{8}$ , then the number of such ${x}_{1}$ is:-
(a) 0
(b) 1
(c) 2
(d) 3

The answer is (b).

First of please tell me the function and how did you get it (I mean what approach did you follow to get this function).
Secondly, please give the value of ${x}_{1}$ that satisfies the equation in the given question.

Please explain it in detail. I will be grateful.

Share this article on:

Comments (4)

pink_ele

Blazing goIITian

Joined: 16 Jan 2007

Posts: 1836

24 Mar 2009 08:25:13 IST

Like 3 people liked this

V=f(x)=pi r^2x......

now expressing r in terms of R and x ....

when x=x1

solving for x1 we get ......

2 values of which one is negative ......so only one x1 is possible.....

value i am getting is......

XYZ

Hot goIITian

Joined: 18 Jan 2009

Posts: 193

24 Mar 2009 11:21:41 IST

Like 1 people liked this

Pink_ele, the function that you have given is absolutely correct.

Aapko nahin lagta ki that you have missed out R in the answer given.

I was getting . But the tragedy here is that the answer given is . I don't understand how has this answer come.

Can you explain???

Please help??? I will be very thankful. (Not to mention, rates assured. A hat waiting from my side.)

pink_ele

Blazing goIITian

Joined: 16 Jan 2007

Posts: 1836

24 Mar 2009 11:28:29 IST

Like 1 people liked this

then being very sure i can say 1 thing..........it shud be x^3/8 and not x^2.....u can check....:)

XYZ

Hot goIITian

Joined: 18 Jan 2009

Posts: 193

24 Mar 2009 11:40:53 IST

Like 0 people liked this

Yes, it can be true as it satisfies all the conditions as well as the answer. So, I think there would be a printing error in the book.

Secondly, about the R thing. Am I correct regarding it??? I mean to say that the answer that I have given is correct or not (keeping in mind the original question)??? Because i think you have missed out on R.

Thanks a lot for your help. I sincerely thank you. Two hats from my side.

May god bless you!!!

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team