Expand the radius of the base surface of a cone to 2 times the original height, and its volume is

4 times, because the radius is expanded to 2 times, the base area becomes 4 times the original.

Cone volume = height * base area * 1 3

If the height remains the same, the base area becomes four times, so the volume also becomes four times the original.

The volume of the cone = one-third of the bottom area of the cone The height of the cone, the letter indicates that it is v=1 3 s h

The bottom area of the cone = pi and the square of the radius of the base, the letter indicates that it is s = r

So the volume of the cone = one-third of pi square of the radius of the base surface of the height of the cone, and the letter representation is v=1 3 r h

The title says that the radius of the bottom surface of the cone is expanded to 2 times, that is, r becomes 2r, r 2r, the height remains the same, or h

The enlarged volume v=1 3 2r) h=1 3 4 r h

Enlarged volume Original volume = (1 3 4 r h) (1 3 r h) = 4

In other words, the enlarged volume is 4 times larger.

Answer: Expand the radius of the bottom surface of a cone to 2 times the original height, and its volume is (4) times the original size.

Let the original radius be r, the height be h, and the volume formula is: v=1 3 r h, so the original volume is 1*(1 3 r h), and now is.

1 3 (2r) h = 1 3 4r h, and the adjustment order is 4*(1 3 r h).

So it is 4 times the original.

Fourfold. Suppose the original cone radius is 3 and the volume is, and now the radius is 6 and the volume is and the volume is 4 times the original.

4 times, the conic volume formula 1 3 times the base area multiplied by the height.

4 times, the square of the radius, assuming that the original radius is 1 and the area is 1, now the radius is 2 and the area is 2 times the square of 2, i.e. 4. 4 divided by 1 equals 4, so it's four times.

4 times, v = pai * pai * r * r * h * 1 3, r increases by two times, the height remains the same, and the volume becomes 4 times.

The answer is 4 times, and the process can't be played.

According to the formula v=1 3sh, while the radius changes r times, the area changes r squares, so it is 4 times.

The radius of the bottom surface is expanded by 3 times, and the height is unchanged, and the volume is expanded by the radius by 3 9 times. Because r h 1 3 is used to calculate the volume, when r is enlarged by 3 times, the base area will be expanded by 9 times, and the volume will be increased by 9 times.

The volume of the cone, the floor area, is 3 r h 3 high. When the radius of the bottom surface is copied to 3 times the original and the height remains the same, the volume expands to 3 9 times the original.

The formula for calculating the volume of a conic is:

v=1 3 base area high.

Let the radius of the original cone be a and the height be h, then the volume of the cone is:

v=1/3·πa²·h=1/3πa²h

The volume of the cone with a 3-fold increase in radius:

v=1/3·π（3a）²·h

3 a h As mentioned above, the radius of the cone is expanded by a factor of 3 and the volume is expanded by a factor of 9.

According to this formula, the radius is multiplied by the height multiplied by 1 3, so it is expanded by a factor of 9.

The radius of the bottom surface of the cone is increased to 3 times, and the height remains the same, and the volume is increased to 9 times.

Suppose the radius is r=1 and expands to 3 times according to the title, and r=3 assumes that the height is 1, then the volume of the two is v= r h= 1 1 =v= r h= 3 1=3

From 3 to 3, it has become 9 times the original size.

Then the original volume is $v 1 = frac pi r 2 h$.

After the radius of the base area is expanded to three times the original, the new base radius is $3r$, and the height is still $h$, then the volume of the new minqi is $v 2 = frac Qiao Naling pi (3r) 2 h = 9( frac pi r 2 h) = 9v 1$.

As a result, the volume of the cone expands to a factor of $9.

Let the original bottom radius of the cone be r and the height be h, then the original volume is:

v1 = 1/3 * r^2 * h

When the radius of the bottom area is expanded to three times of the original, and the radius of the new bottom cover is 3r, then the new volume is:

v2 = 1 3 * 3r) 2 * h = 9 * v1 Therefore, the volumetric ridge of the cone expands to 9 times.

Then the original volume is:

v1 = 1/3)πr^2h

After enlarging the bottom surface, the new bottom surface has a radius of 3r, the height remains the same, and the new volume is:

Bending v2 = 1 3) (3r) 2h = 9(1 3) r 2h = 3 r 2(3h).

Therefore, by enlarging the base area, the volume of the cone is tripled. i.e. v2 v1 = 3.

Do the math yourself.

First: After the change:

The radius will be expanded to 4 times, and the volume will be expanded to 4 4 16 times.

Cone volume formula.

v= (1/3)π(r^2)h

Explanation of the formula: n is the number of the angle system, is the pi, approximately equal, r is the radius of the base circle, and r is the height of the cone.

The volume has been expanded to 9 times.

The volume formula of the cone is v=1 3 * pi * r 2 * h

The volume of the cone is proportional to the square of the radius of the base surface of the cone.

Conic volume: v=sh3= rh3

h unchanged, r = 3r, v = (3r) h 3 = 9 r h 39 r h 3: r h 3 = 9: 1

It has been expanded to 9 times its size.

The radius is expanded by a factor of 3, the diameter is expanded by a factor of three, and the area is expanded by a square multiple of it, answer. 9 times.

Enlarge to 9 times as much as the original because the volume formula of the cone is v=1 3 * pi * r 2 * h

The volume of the non-conic = the bottom area is 3 high

The volume of the cone is proportional to the square of the radius of the bottom surface, so if the radius of the base surface is expanded to 2 times, the volume will be expanded to 4 times.

The radius of the bottom surface of a cone is expanded to 2 times, the height is reduced to 1 3, and its volume is expanded to several times?

Analysis: If the radius of the bottom surface of a cone is expanded to 2 times the original, the base area will be expanded by 2 2 = 4 times.

If the height is reduced to 1 3, then its volume is reduced to its 1 3, so the volume of the cone is expanded to its 4 1 3 = 1 and 1 3 The comprehensive formula: 2 2 1 3 = 1 and 1 3 times.

(2r) square·1 3h = 4 3 r square h, and the volume expands to 4 3 times.

The radius of the base surface is doubled, and the base area is expanded.

Quadruple height is reduced to two-thirds of the original size, which is a two-fold shrinkage.

Twice as large in size.

Analysis: It can be broken down into two steps.

1) The radius of the bottom surface is expanded to 2 times of the original, and the area of the new cone bottom will be expanded by 4 times, so that the volume is 4 times the original, that is, 4x the original volume.

2) For a new cone, if the height is reduced to one-third of the original, then the volume is reduced by one-third, 4x the original volume x one-third = four-thirds of the original volume.

So the volume is expanded by four-thirds.