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cooljackiec

Member

Registered: 2012-12-13

Posts: 186

frustrum and cone

The two bases of a right conical frustum have radii 12 and 9. The two bases are 4 units apart. Let the volume of the frustum be V cubic units and the total surface area of the frustrum be A square units. Find V + A.

A

circular sector with radius 15 is rolled to form a cone. Find the volume of the cone.

Last edited by cooljackiec (2013-07-12 06:12:02)

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I see you have graph paper.
You must be plotting something

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: frustrum and cone

hi cooljackiec,

You did very well from just a few hints last time; so let's see if you can do that again. 

I've put both diagrams together in the screen shot below.

Q1.

I've called the height of the small cone that is not part of the frustrum, x.

By similar triangles

From this you can work out x.

Then you can get the volume of the frustrum by large cone minus small cone.

The curved surface area will be large minus small again.

Add in the area of the top and bottom circles.

Q2.  When you roll that sector around to make a cone, the green line becomes the circumference of the base of the cone.

You know the radius is 15, so you can get the total circumference of the circle and then calculate 288/360 of it for the length of the green line.

Then you can work out the base radius of the cone.

The slant height of the cone will be 15, so you can use pythag to get the perpendicular height.

Then you can calculate the volume.

Hope that helps.

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

cooljackiec

Member

Registered: 2012-12-13

Posts: 186

Re: frustrum and cone

my answer for number 1 is 774pi

and number 2 is 432 pi.

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I see you have graph paper.
You must be plotting something

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: frustrum and cone

hi cooljackiec,

Sorry I didn't reply to this sooner.  I went away the day you posted it and then forgot about it on my return.

I agree with your second answer of 432pi but not the first.

Please would you post the following:

value of x

volume of frustrum

curved surface area of frustrum

top area of frustrum

bottom area of frustrum.

Then I can compare answers and try to work out who is correct.

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

champion999

Member

Registered: 2015-07-01

Posts: 2

Re: frustrum and cone

I also got 774pi for number 1.

value of x: 12
volume of frustrum: 444pi
curved surface area of frustrum: 105pi
top area of frustrum: 81pi
bottom area of frustrum: 144pi

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: frustrum and cone

hi champion999

I have re-worked this and I agree completely with all your answers.  No idea what went wrong before.  Maybe I only had V or only A.  I dislike questions that get you to condense answers like this.  If you get one correct but not the other you get no marks instead of half marks.  And no clues about what you did wrong.  I think it's just a lazy way to use a computer to mark the answers rather than doing it properly.

Anyway, thanks for your contribution.

Bob

That's the second time this week.  Oh dear!  At least I'm getting them right now, so I can dismiss senility.    You are not by any chance related to championmathsgirl are you?

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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