Notes for Frustums

A frustum of a cone is the part that remains when thevertex is cut off by a plane parallel to its base.

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18 em

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1. How is the cut-off cone related to the original cone?~

2. What is the similarity ratio for the two cones? 0-/33. Use the similarity ratio to find the height of thecutoff cone. \ {p c vn t":. ~4. What is the height of the frustum? 8' CVV\

5. Can you find the surface area of the frustum bysubtracting the surface area of the cut-off cone from thesurface area of the original cone? _h•...•..•.Q,,-O-__ -'--_

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6. Can you find the volume of the frustum bysubtracting the volume of the cut-off cone from thevolume of the original cone? -.loj'&I-.le-"'-..;1S'------

7. Find the volume of the frustum to the nearest tenth.\I~i't-:~(3~'t'rr)~'+::..?5q~Ji\jt=-:"l~~4-ljf s\/-\-o -:.~ ( \4 q 'K) I (P';. '1i» 811 ~ 5 7~O.2>em8. Iffou cut along the slant height of the original coneand then unwrap the lateral area of the frustum, what

.\ Itshape will it be? ; sos tw-o.-f . Find the lateralarea of the frustrum. ----------

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A frustum of a pyramid is the part that remains whenthe vertex is cut off by a plane parallel to its base.

Original i;',s~~e-based Pyramid

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26 in,.

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20 in.

1. How is the cut-off pyramid related to the originalpyramid? ~

2. What is the similarity ratio for the two pyramids?'/;;...

3. What is the ratio of the volume of the cut-offpyramid to the original pyramid? \ Ik'

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4. If the volume of the original pyramid is 256 ern.', ?f - ~bfind the volume of the eut-offpyramid. ~;2c~What is the volume of the frustum? ~~ Li em~

5. What is the ratio of the volume of the frustum to theoriginal pyramid? 1f 8'

6. The ratios in (3) and (5) must add up to __ -'---_

7. What shape are the lateral faces of the frustum?ieo ~ t-(a.r

8. If the lateral edge of the original pyramid is 26 in.,find the height of the trapezoidal lateral faces.

\.:L . Find the LA for the frustum.10 ~ \ I <r: -~-r==. \V'O-{':: z:.L\2.. A...\O+ 2.0 )::. H?

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9. Find the surface area of the frustum. \ ad..O ~\De -e, \D"1..::. \00

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5 X:. soExample 1Find the exact volume and find the surface area to the nearest whole number.

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SA -=- 5STt15 + 7~1\ ~ it, \ ~ e.'M?

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Example 3 - A frustum is formed by slicing a coneparallel to its base. The ratio of the heights of thecutoff cone to the original cone is 3:5. If the volumeof the original cone is 625 cu. in., what is the volumeof the frustum? 0 3~: 5

Example 4 - A frustum is formed by slicing asquare-based pyramid parallel to its base and

_.bisecting the height of the pyramid. If the lateralarea 01 tHe orlgmal pyramid is 400 sq. in., what isthe lateral area of the frustum?

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