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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bob bundy
2013-07-28 23:14:01

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

cooljackiec
2013-07-13 11:55:54

my answer for number 1 is 774pi

and number 2 is 432 pi.

bob bundy
2013-07-13 04:33:38

hi cooljackiec,

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

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

cooljackiec
2013-07-13 04:11:41

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.

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