Geometry: An Interactive Journey to Mastery

G௘ͽ îͼ௘௘ͽ^3 = 27.

H௘ͽ ©¹ ̈ ̧§· 121 3 |

I௘ͽ $UHD î IW^2  î LQ^2.

Number of tiles | 25   tiles.

 &RVW î 

J௘ͽ ͼ௘௘ͽ^2  FP^2.

K௘ͽ V 1  ͼ௘௘ͽ^3 in^3 and V 2 = 800 in^3. So, k^3 = 12^3 , and k = 12.

6. 
   

   k = 2.
   D௘ͽ V = 20k^3  Â IW^3.
   E௘ͽ Vbottom í IW^3.

   
   


7. 
   

   D௘ͽ k   20 5 ͼ௘RUk (^5) ௘ͽ
   E௘ͽ k^2 1625.
   F௘ͽ k^2 1625.
   G௘ͽ 6XSSRVHWKDWWKHODWHUDODUHDRIWKHWRSFRQHLVA.
   Then, the lateral area of the entire cone is 25 9 Ak^2 1625 A, so the lateral area of the bottom portion is
   16 AA 16 A.^
   The ratio of the two lateral areas, top over bottom, is 9 169.
   16

   
   

A

A^

H௘ͽ 6XSSRVHWKDWWKHYROXPHRIWKHWRSFRQHLVV.

Then, the volume of the entire cone is 125 61 Vk^3 125 V, so the volume of the bottom portion is

VV V.^

The ratio of the two volumes, top over bottom, is 61  61.



V

V^