Frustum of cone question and enlargement of triangle length. pic included - gcse math

**lFrenzied** · May 30th 2011, 01:23 PM

Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting - frustum of cone

Image - TinyPic - Free Image Hosting, Photo Sharing & Video Hosting - triangle question

At a complete loss. Please do not simply tell me the answer, but give me a step-by-step process of how you got to that answer.

**Wilmer** · May 30th 2011, 05:12 PM

That "triangle" is NOT a triangle!
Agree with y = 2.5; that leaves a triangle dimensions 3.5-7-11 which is impossible...OK?

**Wilmer** · May 30th 2011, 06:15 PM

On the cone problem.
I assume you know the volume of a cone = pi r^2 h / 3

volume larger cone = pi r^2 2h / 3 = 360 ; simplify to get: p1 r^2 = 540 [1]

volume smaller cone = pi (r/2)^2 h ; simplify, substitute [1] to get volume = 45

cup volume is difference...OK?

**Soroban** · May 30th 2011, 06:17 PM

Hello, lFrenzied!

Frustum of cone

The a diagram shows a paper cup of height $h.$
It is part of a cone of height $2h$ and volume $360\text{ cm}^2.$

Find the volume of the cup.

Code:

      :       :  2r   :
      *-------+-------* -
       *      :      *  :
        *    h:     *   :
         *    : r  *    :
          *---+---*    2h
           *  :  *      :
            *h: *       :
             *:*        :
              *         -

$\text{The volume of the entire cone is: }\:V_1 \:=\:\tfrac{\pi}{3}(2r)^2(2h) \:=\:\tfrac{8\pi}{3}r^2h\text{ cm}^3$

$\text{The volume of the small cone is: }\:V_2 \:=\:\tfrac{\pi}{3}(r^2)(h) \:=\:\tfrac{\pi}{3}r^2h\text{ cm}^3$

$\text{The volume of the cup is: }\:V \:=\:V_1 - V_2 \:=\:\tfrac{8\pi}{3}r^2h - \tfrac{\pi}{3}r^2h \:=\:\tfrac{7\pi}{3}r^2h\text{ cm}^3$

$\text{We see that the cup has }\tfrac{7}{8}\text{ the volume of the entire cone.}$

$\text{Therefore: }\;V \;=\;\tfrac{7}{8}(360) \:=\:315\text{ cm}^3.$

**bjhopper** · May 31st 2011, 03:40 AM

Another way
V of smaller cone / V of larger cone= (1/2 r )^2*h / r^2*2h = 1/8 Cup = 7/8 of 360

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Frustum of cone question and enlargement of triangle length. pic included - gcse math

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