Reasoning A cone with radius 3 and height 10 has its radius tripled. How many times greater is the volume of the larger cone than the smaller cone? Use pencil and paper.
Explain how the volume of the cone would change if the radius were divided by three.
The volume of the larger cone is times greater than the volume of the smaller
cone.

9 times larger and 9 times smaller (it changes by the square of the change factor of the radius).

Step-by-step explanation:

the reason :

the formula of the volume of a cone is base area times height divided by 3.

and the base area is the area of a circle with radius r.

=> Vc = pi×r²×height / 3

now, when we multiply r by a factor, like in our examples here by 3 and also by 1/3, then this factor also gets squared in the calculation of that formula.

so, if the new radius is 3×r, then the formula looks like

Vc = pi×(3r)²×height / 3 = pi×9r²×height / 3

so, as you can see, when we triple the radius, we introduce the factor 9 (square of 3) into the volume, and therefore the volume increases by the factor 9.

similar, when we divide the radius by 3

Vc = pi×(r/3)²×height / 3 = pi×(r²/9)×height / 3

we introduce the factor 1/9 into the volume, and it decreases to 1/9th of its original size.

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

25 questions , because they start with 100.  

350-100=250 .  

. 250/10=25

step-by-step explanation:

first take off 100, then what x 10 = 250? that is your answer. (25)