Formulas for the surface area and volume of the cylinder conic Push to the process Math Diary 5

Let their base radius be r and their height be h.

Cylinder volume: r 2h (cylinder volume equal to base area multiplied by height) cylinder surface area: 2 r 2+2 rh = 2 r (r + h) (bottom area plus side area).

Cone volume: 1 3 r 2h

Conical surface area: r 2 + 1 2 2rl = r(r + l) (l is the length of the busbar, equal to the square of r under the root number plus the square of h).

The side of the cylinder is a rectangle, the length of the rectangle is the circumference of the circle at the bottom of the cylinder, and the width is the height of the cylinder, so the area of the cylindrical side is: 2pi*r*h, and the area of the two bases is 2pi*(the square of r).

Cylindrical surface area: base area + side area = 2pi*r*h + 2pi*r*r Cylindrical volume: base area * height = pi*r*r*h The side of the vertebra is a fan, and the circumference of the circle corresponding to the side sector is 2pi*h In fact, the arc length of the sector is the circumference of the bottom circle:

2pi*r, then the ratio of the sector to the circle is (2pi*r) (2pi*h) = r h, and the area of the complete circle is pi*h*h

Then the sector area: pi*h*h*(r h)=pi*h*r, the surface area is equal to the bottom area + side area: pi*r*r+pi*h*r=pi*r*(h+r).

Sorry, I forgot how to derive the volume.

Cylindrical volume formula: base area is high.

Surface area: The square of the radius of the base edge height of the bottom edge.

Cone volume: 1 3 base area high.

Surface area: 1 2 Bottom perimeter Busbar Square of the radius of the bottom surface.

First understand the conical busbar, the conical bus can be understood in this way: the line segment from the apex of the cone to any point on the bottom circle is called the conical busbar, which is represented by the letter L. Subtract the sides of the cone along the conical busbar and give a fan.

If you want to know the area of the fan, you must know the degree of the central angle of the fan, we set the number of the angle of the center of the circle as n degrees, and extend it with another formula of the area of the circle, the area of the circle = the circumference of the circle 2 * radius, and then expand, so the area of the fan = half of the arc length * radius = the square of n 180 * r, but the conical fan does not give the central angle, what should I do? When we look closely, we find that the arc length of the sector is the circumference of the circle at the bottom.

So, the formula is 2 r 2 * sector radius = r * radius, and the sector radius is the length of the conical busbar, so.

S side = rl, combined with the area of the bottom circle, so.

s cone = rl + r squared.

We're here to answer your questions and hopefully make you more aware of the relationship! Because the vertices of the cone are equal to each point on the bottom circle (this is the bus length), the sides of the cone are fan-shaped. (If it's still a circle, it's stuck to the bottom, and it's not a cone, hee-hee-.......)The side view of the cone is a fan, and its area can be used in addition to what you said to find the area

1 2 Arc length Bus length What you are talking about is exactly how we solve the central angle of the graph.

Turn a cylinder into a box (just like a circle is converted into an approximate rectangle), according to the box volume formula.

The base area is multiplied by the height, and the volume of the cylinder = the base area is multiplied by the height.

The relationship between a cylinder of equal height and a conical body of equal height is proved by experiments: a cone.

is one-third of the volume of a cylinder of equal height to the bottom, so: the volume of the cone = the area of the base multiplied by one-third.

Cylinder, divide the cylinder into equal parts and then put it together into an approximate cuboid, and then use the volume formula of the cuboid to form the bottom area into a height, that is, the volume of the cylinder. The cone is regarded as a cylinder of equal height to its base, and the volume of this cone is 1/3 of the volume of the cylinder of equal height to the other base

Convert a cylinder into a box (just like a circle is converted into an approximate rectangle), and according to the formula for the volume of the box: base area times height, the cylinder volume = base area times height.

Through experiments, it is proved that the relationship between a cylinder of equal height and a cone: the cone is one-third of the volume of the cylinder of equal height and other equal heights, so the volume of the cone = the base area multiplied by the height is one-third.

Round d = 2r , s = r 2

Cone d = 2r , s = r 2, v = sh 3 diamond d = four times the four sides and one side, s = half the product of the diagonal length, four times the circumference of the square four sides and one side, area square square of the length of the sides.

Perimeter, area, and volume of the graph:

Circumference (length of outer perimeter).

c = the sum of the three lengths.

c Rectangle = (length + width) 2

c parallelogram = 2 times the sum of the length of the two adjacent sides.

cSquare = side length 4

c diamond = side length 4

c circle = 2 r (r is the radius) = d (d is the diameter) c trapezoidal = two base lengths + two waist lengths.

Area s = base height 2

s rectangle = length and width.

s parallelogram = base height.

s square = square of the side length.

s diamond = half of the product of the diagonal.

s circle = r2 (r is the radius).

s trapezoidal = (upper bottom + lower bottom) high 2

The formula for calculating a cylinder is as follows:

Cylinder side area formula: side area = bottom surface circumference height s side c bottom cherry heng h cylinder surface area formula: surface area = 2 r2 + bottom circumference s s table s bottom brother + c bottom h

Volume formula of a cylinder: volume = base area height v cylinder s bottom h volume formula of a cuboid:

The volume of the box = length, width, and height.

If a, b, and h are used to represent the length, width, and height of the cuboid, the formula is: v length = surface area of the abh cube formula:

Surface area Ridge length Ridge length 6 s positive a 2 6

Volume formula for a cube:

The volume of the cube Ridge length Ridge length Ridge length

If Envy uses a to denote the edge length of the cube, then the volume formula of the cube is v a·a·a a 3

The volume of the cone = 1 3 The area of the bottom surface of the height v The cone 1 3 s The bottom h is all here.

The volume of the cylinder: v = sh The volume of the cone v = 1 3sh

1. Calculation of the surface area of the cone: surface area = bottom area + side area (r = radius, l = busbar, = pi) that is, surface area = ·r2 + ?·2πr·l=π·r2+πrl=πr·（l+r）。

In addition to the calculation of the surface area of the cone, the volume formula for the cone is one-third of the base area multiplied by the height, which is expressed by letters as 1 3 r2h.

2. The surface area of the cylinder = 2 r(r+h), the volume of the cylinder = r 2h, where r represents the radius of the bottom surface of the cylinder, and h represents the height of the cylinder.

Summary. The derivation process of the side area formula: the side area of the cylinder = perimeter x height perimeter = the length and height of the rectangle = the width of the rectangle, the side area of the cylinder = the area of the rectangle = length x width.

The formula for the side area and volume of the cylinder is pushed to the process. and the volume of the conic is pushed to the process.

The derivation process of the side area formula is as follows: the side posture product of the cylinder = perimeter x height perimeter = the length of the rectangle = the width of the rectangular square and the side area of the cylinder = the area of the rectangle = length x width.

Volume formula derivation process: Derivation of cylindrical volume formula: It is derived by the method of transformation.

First, divide the bottom surface of the cylinder into a number of even small sectors, and then cut these fans along the height of the cylinder and put them together to obtain an approximate cuboid, so that we can convert the cylinder into a cuboid. The bottom area of the closed bucket of this boxy is the bottom area of the cylinder, and the height of the cuboid is the height of the cylinder, because we know that the volume of the cuboid = length, width, height = base area height. In this way, it is deduced that the volume of the cylinder = the height of the base area.

The cylinder volume formula is the formula used to calculate the volume of a cylinder.

The derivation process of the volume formula of the cone: The derivation process of the volume formula of the cone is as follows: the area of the bottom δaba' and δb'a'b of the triangular pyramid is equal and the height is also equal (the top core is c).

The area of the bottom δb'cb' and δc'b'c of the triangular pyramid is equal, and the height is also equal. (The vertices are all a'). v1=v2=v3=1 3v triangular prism.

v prism sh. v triangular pyramid = 1 3sh.