Geometry: An Interactive Journey to Mastery

3. If the radius of the sphere is r, then the side of the cube is 2rͼ௘'UDZDSLFWXUHWRVHHWKLV௘ͽ

Probability =

33

23

 33 

2 SSrrr^8 r  SS.^

4. Probability = 30 60SSSu^5252 180072.


5. Let r be the radius of the circle.
   Note the half equilateral triangle in Figure S.25.1 with
   hypotenuse rͼ௘DQGKHQFHZLWKRQHOHJ 2 r and the other

(^223).
r  rr · ̧¹^
$UHDRIWKHFLUFOH ʌr^2.
Area of the triangle
2
(^112222) base height 2 3
(^13) 3.^33
r r r
rrr
u u §· ̈ ̧§· ̈ ̧©¹
©¹
Probability
22
2
(^33)  (^33) 
SSrrSr (^) SSS.

6. We have that approximately 1000875 ; that is, 0.875 of the photograph represents oil.
   %HFDXVHWKHWRWDODUHDUHSUHVHQWHGE\WKHSKRWRJUDSKLVVTXDUHNLORPHWHUVWKHDUHDRIWKHVSLOOLV
   DSSUR[LPDWHO\î NP^2.


7. 100, 000 ˜uu     IW ^3


8. You need to estimate the volume of the room and the volume of your head
   to compute this probability.


9. The probability we seek is SS ^32 .௘6HHFigure S.25.2௘ͽ

(^2) r 2 30° 3
r r
Figure S.25.1

33

33

3

3

3

3

Figure S.25.2