How to calculate the volume of a ball and how to calculate the volume of a ball?

Let the radius of the ball be r, divide the radius oan equally, and level the points above these points.

The surface cuts the hemisphere into n layers, each of which is "small" in an approximate cylindrical shape.

Discs", the sum of the volumes of these "small discs" is the volume of the hemisphere.

Since the "small disc" is approximately cylindrical in shape, it is also close in volume.

Resembles the volume of a cylinder. Its height is the thickness of the "small disc".

From the Pythagorean theorem, the radius of the lower bottom surface of the "small disc" of the ith layer (counted from the bottom up) is obtained:

As the number of layers is increasing, that is, as n is getting larger, the equation is getting closer and closer to the hemispheric.

The volume, if n becomes infinitely larger, can be extended from the formula to the volume of the radius.

You can go to the library and see it!! This is only pushed in advanced mathematics in college, and in high school, you just need to memorize the formula!!

The formula for the volume of a sphere with radius r is: v=(4 3) r or =(1 6) d

This high school has the method of proving the volume of the ball, and you can flip through the high school math and prove it through the method of solid geometry.

The formula for the volume of a sphere with radius r is: v=(4 3) r 3 (four-thirds multiplied by the cubic of the radius).

v=(1 6) d 3 (one-sixth multiplied by the cubic of the diameter).

The surface area of a sphere with radius r is calculated as: s = 4 r 2 (4 times the quadratic of r).

The volume formula of the sphere is: v ball = 4 3 r (r is the radius), the diameter is known to be 3 meters, then the radius is meters, and the formula for the volume is 4 3 * cubic meters (keep 2 decimal places).

Expanding the knowledge, the formula for the surface area of a ball is s-sphere = 4 r

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The bottom surface of the cylinder is circular, and the volume of the cylinder is found. v cylinder = s * h (s is the bottom area of the circle, h is the height of the cylinder) s = r, the formula for the volume is: v cylinder = r h = cubic meter.

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The bottom surface of the cone is the element, and the volume of the cone is calculated: v cone = 1 3sh (s is the area of the bottom surface of the circle, h is the height of the cone) s = r, and the formula for the volume is: v cone = 1 3 r h = 1 3 cubic meters (keep 2 decimal places).

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end precautions.

To find the cube of a circle, we are finding the volume of a circle, first we need to know what is the volume of the figure, spherical, cylindrical or conical, and then calculate it according to the volume formula.

The volume of the ball can be calculated according to the formula: v= r, where v represents the volume and r represents the radius of the ball.

The ball is a rotating body formed by the straight line where the diameter of the semicircle is located, and the surface of the semicircle rotates once, so the radius or diameter of the ball is known, and the volume of the ball can be easily calculated by applying the volume formula.

For example, if the radius of a ball is 5 cm, then v = and the last v is approximately equal to 523 cubic centimeters.

The volume formula of the ball:v=4/3πr^3

Volume:

A circular center of a cylinder with a base radius r and a height of r is excavated to excavate a circular contour of equal base and height. The remaining part is equal to the area of a hemisphere when it is cut in a flat plane. Wait for the conclusion that they are equal in volume.

And the volume of the excavated body is easy to find. It's the volume of the hemisphere. v＝2/3πr^3 。

Hence the volume of a whole sphere is4 3 r 3 and the ball is formed by circular rotation. The area of the circle is s= r 2, then the sphere is its integral, and the formula for finding the volume of the corresponding sphere is v=4 3 r 3

Data Extension:

Surface Area:

Let the circle y (r 2 x 2) rotate about the x-axis to get the sphere x 2 + y 2 + z 2 r 2. Find the surface area of the ball.

With x as the integral variable, the integration limit is [ r,r].

On [ r,r] take a sub-interval [x,x+ x], and the area of the upper part of the ball obtained by this arc around the x-axis is approximately 2 y ds, and ds is the arc length.

So the surface area of the ball is s2 y (1+y'2) DX, tidy it up to get S4 R

The volume formula of the ball:v=4/3πr^3

Volume:

Dig out a contour of the same height in the center of a cylinder with a base radius r and a height of r. The remaining part is equal to the area of a hemisphere when it is cut in a flat plane. Wait for the conclusion that they are equal in volume.

And the volume of the excavated body is easy to find. It's the volume of the hemisphere. v＝2/3πr^3 。

Hence the volume of a whole sphere is4 3 r 3 and the ball is formed by circular rotation. The area of the circle is s= r 2, then the sphere is its integral, and the formula for finding the volume of the corresponding sphere is v=4 3 r 3

Data Extension:

Surface Area:

Let the circle y (r 2 x 2) rotate about the x-axis to get the sphere x 2 + y 2 + z 2 r 2. Find the surface area of the ball.

With x as the integral variable, the integration limit is [ r,r].

On [ r,r] take a sub-interval [x,x+ x], and the area of the upper part of the ball obtained by this arc around the x-axis is approximately 2 y ds, and ds is the arc length.

So the surface area of the ball is s2 y (1+y'2) DX, tidy it up to get S4 R

1. Use this formula: 2. Find the radius. 3. Find the cubic of the radius. 4. Multiply four-thirds by the cubic of the radius. 5. The value of the solution. I really don't know how to calculate the volume of a ball? Here's how to do it.

1. Use this formula: v=??r?.v represents the volume and r represents the radius of the ball.

2. Find the radius. Sometimes you know its radius, and sometimes you may know its diameter. If you know its diameter, just divide it by two (i.e., half the diameter).

Or you know its surface area or some other property. Don't panic, just find the corresponding formula, replace the corresponding value with the one you know, and then solve the equation to figure out its radius.

3. Find the cubic of the radius. Multiply the radius by three times, (radius * radius * radius), note that any value multiplied by three is its cubic power.

4. Multiply four-thirds by the cubic of the radius. You can do the math with a calculator, or you can multiply by four and divide by three, either way. Rock width.

5. The value of the solution. If you want a very accurate value, just add the symbol to the end of your previous answer. Otherwise, use the key on your calculator to get an approximation, and if you don't have the key, use the value instead of if it's an eight-digit calculator.

TipIf you only need to calculate a part of the volume of the ball, say half or a quarter, find the volume of the whole ball, and then multiply it by the fraction of the part you are looking for. For example, if you want to find half of a spherical volume of 8, you can multiply 8 by half, or divide 8 by 2 to get 4.

Note that the "*" symbol is used here instead of the multiplier sign to avoid confusion with the variable x.

Remember to check that all units of measurement are the same. If the units are different, convert the units.

Don't forget to use cubic units. (e.g. cm?.)）。

You need to prepare a calculator (the reason is that it should be troublesome to go back to the problem without a calculator).

First of all, a circle is an object in two-dimensional space, which can only be said to be a surface, and can only calculate the area, and a sphere is an object in three-dimensional space, which is a three-dimensional figure, and can be said to be a volume, and the area of the circle is calculated by the formula: s1 = pi and the square of the radius. Letters can be represented as:

s= r2 or s= *d 2)2 ( for pi, r for radius, d for diameter); The volume of the ball is calculated as: v=4 3 to the third of the radius.

Extended Information]:

Related calculation formulas.

Area of a circle: s = r = d 4;

Sector arc length: l = central angle (radian system) * r = n° r 180° (n is the central angle);

Sector area sensitivity: s=n r 360=lr 2 (l is the arc length of the fan);

Diameter of the circle: d=2r;

Cone side area: s= rl (l is the length of the bus);

The radius of the bottom surface of the cone: r=n° 360°L (L is the length of the busbar) (r is the radius of the bottom surface).

The basic nature of the circle is that the brother rents the brother.

1. Symmetry of the circle.

1) A circle is an axisymmetric figure, and its axis of symmetry is the straight line where the diameter is located.

2) A circle is a centrally symmetrical figure, and its center of symmetry is the center of the circle.

3) Circles are rotationally symmetrical figures.

2. Vertical diameter theorem.

1) Bisect the string perpendicular to the diameter of the string and bisect the two arcs opposite the string.

2) Corollary: The diameter of the bisector chord (non-diameter), perpendicular to the chord and the two arcs opposite the bisecting chord. The diameter of the bisector arc, the chord to which the perpendicular bisector arc is opposed.

3. The degree of the central angle of the circle is equal to the degree of the arc it opposes, and the degree of the circumferential angle is equal to half of the degree of the arc it opposes.

1) The circumferential angle of the same arc is equal.

2) the circumferential angle of the envy of the diameter is a right angle; The circumferential angle is a right angle, and the string it is facing is the diameter.

The volume of the ball. Four-thirds by the cube of the radius of the vulture.

4 3) Vultures 3

The volume of the ball can be calculated by the following formula: v = 4 3) r 3, where v is the volume of the ball, which represents pi and r is the radius of the ball. This formula is very simple, you only need to know the radius of the ball to quickly calculate the volume of the ball.

It is important to note that this formula assumes that the ball is a perfect round sphere. If the shape of the ball is affected by some factors that cause it to be not a perfect ball, then the results calculated using this formula may be incorrect.

In addition to using formulas to calculate the volume of a ball, there are other ways to measure the volume of a ball, such as using the specific gravity method, the flow method, or the weight test to determine the volume of the ball. But these methods are not as quick and convenient as using formulas, especially when the size of the ball is very small or very large, using formulas to calculate is the most reliable and effective method.

The volume of a ball may seem like a simple problem, but it is actually commonly used in physical and engineering calculations, such as when designing water towers, oil tanks, or storage devices, where the volume of a spherical object needs to be accurately measured to ensure that the capacity meets the requirements. In addition, the volume of the ball is an important parameter in the sphere motion model, for example, when calculating basketball, soccer or golf balls, you need to know the volume and weight of the ball. Therefore, it is very important to understand how to calculate the volume of a ball.

To summarize, we can simply calculate the volume of a sphere using the formula v = 4 3) r 3. While there are other ways to measure the volume of a ball, formula calculations are the quickest and most convenient method, especially in large-scale and complex calculations. Knowing how to calculate the volume of a sphere is very important in both physical and engineering calculations, as well as in the model of sphere motion.

Spheroid volume v=4r3

Sphere: The shape composed of all points in space with a distance from the fixed point to the fixed point is called a sphere, as shown in the figure on the right. A sphere is a three-dimensional figure with a continuous surface, and the geometry enclosed by the sphere is called a sphere.

Collection Definitions]:

1The set of points whose distance from the fixed point in space is equal to or less than the fixed length is called a sphere, or a sphere for short.

2. The rotating body formed by rotating the diameter of the semicircle is called a solid sphere, referred to as a ball, with the straight line where the diameter of the semicircle is located as the axis of rotation.

3. The set of points whose distance from the fixed point in space is equal to the fixed length is called a sphere, that is, the surface of the sphere.

4. The center of the ball is called at a fixed point, and the radius of the ball is called by the fixed length.