Similar frustums

The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums?

Correct answer:

x =  6.6667 cm

Step-by-step explanation:

r=8 cm R=32 cm h=10 cm  h=x+y  r:y=m:x  yr=hym  m=r+y/h (Rr)  r (hy)=m y  r(hy)=(r+y/h(Rr))y  8 (10y)=(8+y/10 (328)) y 2.4y216y+80=0 2.4y2+16y80=0  a=2.4;b=16;c=80 D=b24ac=16242.4(80)=1024 D>0  y1,2=2ab±D=4.816±1024 y1,2=3.33333333±6.6666666666667 y1=3.3333333333333 y2=10   Factored form of the equation:  2.4(y3.3333333333333)(y+10)=0  y=y1=3.3333=3103.3333 cm  x=hy=103.3333=3206.6667 cm  m=r+y/h (Rr)=8+3.3333/10 (328)=16 cm   Verifying Solution:  c1=r/y=8/3.3333=512=2.4 c2=m/x=16/6.6667=512=2.4 c1=c2

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Showing 1 comment:
Math Student
m is radius of middle circle = radius of a bottom of upper frustum and radius of top of bottom frustum.





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