CPhill

We can use  similar triangles  to  find  the height of the cone

Let x  be the distance  from the cone's apex to  the  top of the smaller circle

We  have  that

[  x  + radius of smaller circle]           [ radius of larger circle + circum of small circle + x]

_________________________  =   ___________________________________________

     radius of smaller circle                      radius of large circle

[ 1 + x ]         [ 2 + 2 + x]

______   =    _________    cross- multiply

    1                      2

2 [ 1 + x ]  =   1 [ 2 + 2 + x ]

2 + 2x  =  4  + x

x  =  2

So....the  height of the  cone   =   4  + 2  + 2   =  8

Now...x + 1  = 3  is  the hypotenuse of a right triangle  with  one of the legs  =  the radius  of the smaller cone

Let A  be the apex of the cone....B  be  the center of the small circle  and   C  be the point where the radius of the small circle  intersects  the side of the cone

Then sin of angle ABC  =  BC/ AB  =   1 / 3

And the tangent  of  this angle  =  1/ sqrt (8)

And we can find the  radius  of the cone thusly :

tan ABC   =  r / height of cone

1/ sqrt (8)  =  r  /8

8/sqrt (8)  = r  =  sqrt (8)

tan 30°  =  r / 8

1/√ 3  =  r / 8

r  =  8 / √ 3

So....the  volume of the cone  is

(1/3)  pi ( radius)^2 (height)  =

(1/3) pi *(sqrt (8))^2(8)  =  (64/3) pi  units ^3   ≈  67.02  units ^3

Good job, LD    !!!!!

A "Best Answer".....

The easiest way to  do this is to first  find the surface area  of both figures

Surface area  of  larger figure  =

2 ( 8*2  + 14*8  + 14*2]  =   2 [ 16 + 112  + 28]  =  2 [ 156]  =  312 cm^2

Surface area of smaller figure  =

2  [ 8*4  +  6*4  + 8*6]  =  2 [ 32 + 24 + 48]  =  2 [ 104]  =  208 cm^2

From this  we want to  subtract the area of two  8 x 4 rectangles  [the areas  where each of the two objects are touching each other =  2 x 32  =  64 cm^2

So.....the total surface area  = 

[ 312 + 208  -  64 ]  =   456 cm^2

Last one

Circle : Stalls

    2   :    5

5/2  = S/C

(5/2)C  =  S

So  the  number that can possiblt occupy S  = (5/2)(528)  = 1320

But only 2/3 of these showed up  = 880

So  the %   of  occupancy  =    [ 528 + 880 ]  / [528 + 1320]   = 1408 / 1848  = .76  = 76%

Second one.....this one is a little  difficult  !!!

Note  that  the ratio of 2  to 7   is the same as   6 to 21

So the ratio of blue to green  =  6 : 21

And  red : green  =  1 : 3   =    7 : 21

So.....we have the following possibilities

B      R      G          Total

6      7       21          34

12   14      42          68

24   28      84        136

So....the greatest number of red sweets possible   =   24

First one

M    :     W     :    C

17          9         12

Let  the number of women  =  x

So.....the  number of men  = x + 3512

And we know that

W             9

___  =    ____

M             17

So this implies that

9             x

__  =  ________        cross-multiply

17      x + 3512

9 ( x + 3512) = 17x     simplify

9x + 31608  = 17 x        subtract  9x from both sides

31608  =  8x       divide both sides by 8

3951  = x  = the number of women

We also know  that

 C           12         4

___  =    ___  =  __

 W            9         3

So  multiplying both sides of this  by W  we have that

C  = (4/3)W

C = (4/3)3951   = 5268  =   number of children

x / y  = 5/3

This mplies that

x = (5/3)y

And we know that  x + y  =  56

So

(5/3)y + y  = 56

(5/3)y  + (3/3) y  = 56

(8/3)y = 56         mutiply both sides by  3/8

y = 56 (3/8)  =  21

And x = (5/3)y  =  (5/3)(21)  =  35

So

x - y  =  35  - 21   =   14

Let P be the beginning poulation

At the  end of  2005  the  new poulation is   (1.20)P

At the end of  2010, the population was  (1.30) [ (1.20)P]  = 1.56P

So....the poulation increased by  (1.56 - 1)  = .56 =  56%  from 2000 to 2010

Not sure about this....but

A   gcm of 24, 8   = 24

     gcm of 24, 7   = 168        meets the criteria  

B  gcm of 24, 7  = 168

     gcm  of 24 , 8 = 24        does not  meet the criteria

D  gcm  of 24,7=  168

     gcm of 24.,6  = 24       does not meet the criteria

E  gcm of 24,6  = 24

    gcm of 24, 7  = 168    meets the criteria

C gcm 24, 3   = 24

    gcm 24, 2   = 24     gcm's  are the same.....but  gcm of 24,y  >  gcm of 24,x

So this is the one that cannot  be true

So   y/x  cannot equal 2/3

Let  the top  of the clock  = 0°

Every minute the minute hand  moves 6°  [in 60 min it moves 360°]

And every minute the hour hand moves   (1/2)°   [in 60 min it moves 30°...1/12 of a complete rotation ]

So in 48 minutes the minute hand has moved  48*6  = 288° from the top of the clock

And in the same time the  hour hand has moved 48 * (1/2)  = 24°  from the top of the clock

So.....the larger angle formed by the hands = 288 - 24  = 264°

So....the smaller angle  formed  = 360  - 264   = 96°