CPhill

Second.....easier than the first one   !!!

Volume of cone  = (1/3)  3.14  * ( radius of cone)^2 * height of cone  =

(1/3) (3.14) * (2^2) * 6  =     25.12   (1)

Volume of cylinder  = pi * radius^2 * height  =

pi * 2^2 * 12  =      150.72     (2)

So....total volume is    (1) + (2)  =  175.84  in^3

First one

We need to find the height of the pyramid

Cone volume  =  (1/3) (3.14)  * ( radius of cone )^2 * ( height of cone )

1884  =  (1/3) (3.14) * (10)^2 * (height of cone)

1884 = (100/ 3)) (3.14) * height of cone   

Divide both sides by  (100/3) (3.14)

Height of cone  =  1884 /   [ (100/3) (3.14)]  =  18  =  height of pyramid

Volume of (square ) pyramid  =   (1/3)  [ side of base ]^2 * 18  =

(1/3)* ( 20^2] * 18  =  2400 in^3

So....the difference is    2400 - 1884  =     516 in^3

 √ [ 125 x^3 ] 

√25 *  √5 *  √x^2 *  √ x

5  * √5  * x  * √ x

5x √ [ 5x ]

LOL!!!!!

Thanks for that solution,  Dimitristhym.......!!!!

Let the smaller number   = N

The greater number  = 4 times N   = 4N

And we know that 

N + 4N   = 155

5N    = 155      divide both sides by 5

N =  31     [ the smaller number ]

And the larger number is  4 ( 31)  =  124

No prob   !!!

√ [ 128 r^3 ]  =

√64 *  √2 *    √ r^2   *   √ r   =

8 * √2 * r   * √ r  =

8r √ [ 2r ]

Second one

Note that the height of the cylinder  =  2 * radius of the sphere

And the radius of the sphere  =   radius of cylinder

We need to find the radius of the  cylinder

432 pi  =  pi *  radius^2  * height

432 pi  = pi  * ( radius^2) *( 2* radius)      [ divide out 2, pi ]

216  =  radius^3      take the cube root of both sides

6  = radius

So....the volume of the sphere is

(4/3) pi * (radius)^3  =

pi *  (4/3) * 6*3

pi * (4/3) * 216  =

288pi  in^3

First one :

Volume of a cylinder  =  pi * radius^2 * height

Radius of top cylinder  = 24/2  = 12

Height of top cylinder = 60 - 40  = 20

Radius of bottom cylinder  = 30/2  =  15

Height of bottom cylinder =  40

So....total volume  is

pi  [ 12^2 * 20  + 15^2 * 40 ]  =

pi [ 144 * 20  + 225 * 40 ]  =

pi  [ 2880  + 9000 ]  =

pi [ 11880 ]  = 

11880 pi  in^3