CPhill

Area  =   pi * (radius)^2 *  (280/360)  =

pi (250) (280/360)  ≈

610.87 ft^2  =   

611 ft^2

Volume of cone  = 

(1/3)pi *radius^2 * h  = 

(1/3)pi *(10)^2 * h =

(100/3) (3.14) * h =

(314/3) h

We can  find the height of the cone (and pyramid) as follows

1884  = (314/3)h    multiply both sides by (3/314)

1884 (3/314)  = h =  18 cm

Volume of pyramid   =  (1/3)side^2 * height  = (1/3)(20)^2 * 18  =  (400/3) * 18  =  

400 (18/3)  =   400 * 6   =   2400 cm^2

So....the difference in volumes  is   2400 - 1884  = 516 cm^2

Thanks, EP  and AT   !!!!!!

For a large number .....check out  "Graham's Number " here :

https://waitbutwhy.com/2014/11/1000000-grahams-number.html

Warning :  This is mind-blowing  !!!!

The rectangle will have the smallest area  when the  difference between the width and length is the greatest....for a perimeter of 24 we have

24  = 2(W + L)

12  = W + L

 So.....the area is smallest for integer sides of 11 cm and  1 cm

So...the smallest area will be  1 * 11  =   11 cm^2

What is the greatest perimeter you can make for a rectangle with an area of 24 square units?

Assuming integer sides....the gretest perimeter will be  a  24 x 1  rectangle

And the perimeter  is  2(24 + 1)  =   50 units

The radius  is 9in  =  3/4 ft 

The distance that the whell travels in one revolution  is    2pi * (3/4) ft  = (3/2)pi ft = (1.5pi ) ft

The number of feet in a mile  = 5280

So....the number of revolutions it makes is

5280 /[ 1.5pi ]  ≈     1120 revolutions

Sorry, guest....my bad.....thanx for the better eyesight....LOL!!!!

40.

For a parallelogram,  Angle  ABC   +  Angle DAB  =  180

So

64   + 4y  -  12  =  180       

52 + 4y  = 180     subtract 52 from both sides

4y  = 128  divide both sides by 4

y  = 32

Also..for a paralleogram

AE  = EC

3x  - 5  =  16

x  = 21

x  = 7

Arc  Length  =  radius *  central angle  (in rads)

So we have

6  = radius  * (2/5)pi

6 (5/2) / pi  =  radius  =   30/pi ≈  9.55 m

y  = x^2  - 5

Let the point on the parabola  be  (x, x^2 - 5)

The distance, D, between this point and the origin can be represented by :

D  = sqrt  [  x^2  +  ( x^2 - 5)^2 ]

D  = sqrt [ x^2 + x^4 - 10x^2 + 25]

D  = [ x^4 - 9x^2 + 25 ]^(1/2)

Take the derivative of this and set to 0

D'  =  [(1/2] [(x^4 - 9x^2 + 25 ]^(-1/2)* (4x^3 - 18x)  = 0

This will equal 0  when  (4x^3 - 18x)  = 0       factor  this

2x (2x^2 - 9)  = 0

Set both factors to 0   and solve for x

2x  =  0                     2x^2  - 9  = 0

x  = 0                         2x^2  =  9

reject                           x^2 = 9/2

So....the distance, D, is

D  = sqrt  [ (9/2)^2 - 9(9/2) + 25 ]  =  sqrt [  81/4 - 81/2 + 25 ] =

sqrt [ 81/ 4 - 162/4  + 100/4]  =

sqrt  [ 81 - 162 + 100]  / 2  =

sqrt  [ 19 ] /2

So....a +  b  =   19 + 2   =  21