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niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

slant height of cone

this ques. is based upon vol. and surface area.
the ques is an MCQ one.

Q.slant height of the cone of which the frustum is a part ,is equal to

options:-

a) hr1/(r1-r2)

b) lr1/(r1-r2)

c) (h+l)r1/(r1-r2)

d) h(r1+r2)/(r1-r2)

please help me out along with the process to solve this.

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friendship is tan 90°.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: slant height of cone

hi niharika_kumar

This is a bit tricky without the diagram or any explanation of what each letter stands for.

Below I've posted a diagram with some distances marked.  Can you do the same?

You may be able to work with similar triangles.

Let's say that the top cone has a height x, a slant height y and a radius r2 and for the whole cone, height x+h, slant height y + L, radius r1.

Then

and

I cannot match any of these answers yet so I need more information if I'm to give you any more help. 

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: slant height of cone

Hi

If Bob's labels are correct I'd go for a).

Bob: You are using the wrong triangles. Use the big one and the small one with base of r1-r2 and height equal to the height of the frustum.

Last edited by anonimnystefy (2013-10-11 11:01:21)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: slant height of cone

thnx bob and anonimystefy but there is nothing extra info. given apart frm what i mentioned above . And i tried but couldn't figure it out.
all i can say is that in the book the answer is given as option b). pls see if you can bring it out using some methods .

---

friendship is tan 90°.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: slant height of cone

hi niharika_kumar

There must be information to say what all those letters stand for.  Is there a diagram as part of an earlier question?

I'm sure that this question requires the use of similar triangles.  That's the way to get a formula involving the distances from the whole cone and the cone that is chopped off to make a frustrum. 

I can get to

using my second diagram.  That looks quite a bit like answer b except r2 rather than r1.  But for r1 - r2 to be positive r1 must be the radius of the larger base, so I'm still puzzled.

anonimnystefy:

It comes to the same thing; either way you get an expression with r1 - r2.

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

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: slant height of cone

i completely agree with u bob , i think the options printed there are wrong.
thnk u for helping

---

friendship is tan 90°.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: slant height of cone

hi niharika_kumar

There must be information to say what all those letters stand for.  Is there a diagram as part of an earlier question?

I'm sure that this question requires the use of similar triangles.  That's the way to get a formula involving the distances from the whole cone and the cone that is chopped off to make a frustrum. 

I can get to

using my second diagram.  That looks quite a bit like answer b except r2 rather than r1.  But for r1 - r2 to be positive r1 must be the radius of the larger base, so I'm still puzzled.

anonimnystefy:

It comes to the same thing; either way you get an expression with r1 - r2.

Bob

Aren't we looking for L+y, not just y?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: slant height of cone

Aren't we looking for L+y, not just y?

Who knows? 

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

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: slant height of cone

Well, L+y is the slant height of the whole cone, right?

---

“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

niharika_kumar

Member

From: Numeraland

Registered: 2013-02-12

Posts: 1,062

Re: slant height of cone

Well, L+y is the slant height of the whole cone, right?

as per bob's diagram, YES.

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friendship is tan 90°.