Volume and Surface Area Calculator: Calculate the volume and surface area of various geometric shapes, including the barrel, cone, frustum cone, cube, cylinder, hollow cylinder, sectioned cylinder, parallelepiped, hexagonal prism, pyramid, frustum pyramid, sphere, spherical cap, spherical sector, spherical zone, and torus. Enter the measurements for the specific shape and the calculator will provide the corresponding volume and surface area.
Whenever there is a question of total area, this implies that we must take into account all the faces of the solid and add their respective areas.
The volume of the circular base cone is one-third of the product of the area of the base times the height.
V = (Ab.h)/3 where h = the height of the cone. Ab=the area of the base
The area of the cube is expressed in the unit of measure of side length c squared. Example: if the length c is expressed in centimeters (cm), then the area of the cube will be expressed in cm².
Principle of calculating the area of a cube A cube has 6 sides (like a dice to throw). Each of these faces is a square whose area is equal to c² (formula for calculating the area of a square).
The area A of a cube of which c is the measure of the sides is therefore equal to:
A = 6c²
To determine its volume, we must rely on the dimensions of its base as well as its height. In the case of the cube, these measurements are the same. Thus, we can deduce the following formula:
the volume of the cube = c3 where c = measure of an edge.
the volume of the cube is expressed in the unit of measure of side length c cubed. Example: if the length c is expressed in centimeters (cm), the volume of the cube will then be expressed in cm³.
In this way, we can calculate the space occupied by a cube, regardless of the situation.
The volume of a cylinder corresponds to space it occupies in its environment. Even if this solid is not part of the family of prisms, its formula for calculating its volume is the same as this.
V = πr² × h where:
h = height of the cylinder
r = radius of the base
The Volume of a Frustum of A Cone is given by the formula:
Volume of a Frustum of A Cone = (π / 3).h.(R2 + r2 + r.R)
Our calculator uses this formula and makes it possible to quickly obtain the Volume of a Frustum of A Cone according to its height and the radii of each of its bases.
R= The radius of the cone
r= the radius of the Frustum cone
h= height of the Frustum cone
The volume of a Frustum of a pyramid is the product of its height by the arithmetic mean of the areas of its bases and their geometric mean. The volume V of the Frustum is expressed by the general formula:
V = h/3 (S + s + √ S.s)
where h is the height of the Frustum between the two parallel planes, and S and s are the areas of the bases of the Frustum (contained in the parallel planes of the section of the solid.
You must use the formula for the volume of an irregular prism in order to find the volume of a hexagonal prism. The volume of a prism irregularity is equal to the area of the base times the height of the prism. Once you do this area calculation, then multiply the result by the height of the prism.
side length: a
the height: h
Hence the formula:
the volume of the Hexagonal prism V = (3 √ 3)/2 . a² .h
Note: All dimensions must be expressed in the same unit of length, before performing a calculation!
Principle of calculating the volume of a hollow cylinder The volume of a solid cylinder of diameter D and height h is calculated from the following formula:
A = (π / 4). D². h
To calculate the volume of a hollow cylinder, simply subtract from the volume of the outer cylinder the volume of the inner cylinder. Its volume V is therefore equal to:
A = (π / 4 . D² . h) - (π / 4 . d² . h) = π / 4 . h . (D² - d²)
The volume of a Parallelepiped corresponds to space it occupies in its environment.
We design :
The Length: a
The Width: c
The depth: b
Hence the formula:
the volume of the Parallelepiped V = a. b .c
Note: All dimensions must be expressed in the same unit of length, before performing a calculation!
The total area of a pyramid is obtained by adding its lateral area and the area of its base.
lateral area: AL
Base area: AB
Hence the formula for calculating the total area AT of a pyramid:
AT = AL + AB
Since this polyhedron is formed by only one base, the formula of its volume will be different from that of prisms.
The volume of a pyramid is calculated by multiplying the area of its base by the length of its height and then dividing the result by 3:
Volume of pyramid = (Area of the base x height)/ 3
To calculate the volume of a sectioned cylinder, you must perform the following equation:
π pi (which is 3.14) multiplied by the square of the radius multiplied by the (height 1 + height 2) divided by 2
The formula is, therefore:
Volume of a sectioned cylinder = π . r² . (h1 + h2) / 2
The smallest height is represented by h1, while the tallest by h2.
To calculate the area of a sectioned cylinder, you must perform the following equation:
π pi (which is 3.14) multiplied by the radius multiplied by the (height 1 + height 2)
The formula is, therefore:
Area of a sectioned cylinder = π . r . (h1 + h2)
The smallest height is represented by h1, while the tallest by h2.
1 Litre is equal to 0.001 m³. We can also define that 1 m³ is equal to 1000 liters. So if we use the formula for calculating a volume which is: length x width x height and convert the result, we get a volume in liters. For example, consider a swimming pool that is 10m in length, 3m in width and 2m in depth (we assume that the depth is equal over the entire length of the pool). The formula will therefore be:
10 x 3 x 2 = 60 m³ If we convert this result into liters we get: 60 m³ = 60,000 liters
Although it is entirely composed of a single curved surface, it is possible to calculate the area of the sphere.
A = 4 . π . r² where r = measure of the radius
From its curved surface, we can see a certain resemblance between this formula and that allowing to calculate the area of a disc. Thus, only one measurement is essential to allow the use of this formula, namely the measurement of the radius.
The volume of a Sphere corresponds to the space inside the sphere which delimits it. To find its volume, just apply this formula:
V = 4 . π .r3 with r = measure of the radius
Once again, only the radius measurement is necessary to complete the process.
The volume delimited by a spherical cap of height h and the sphere of radius r is:
V = π .r2 (r - h/3)
The volume V of a spherical sector corresponding to a spherical cap of height h in a ball of radius r is given by the relationship:
V = (2 . π .r2 .h)/3
The area of a spherical zone or of a spherical cap is given by the following formula:
A = 2π .r .h
in which :
r is the radius of the sphere;
h is the distance between the two parallel planes.
The volume V of a spherical Zone corresponding to a spherical cap of height h in a ball of radius r is given by the relationship:
V = π h / 6 (3R2 + 3r2 + h2)
in which :
h: height of the zone
a: large radius
b: small radius
Johannes KEPLER (German mathematician and astronomer, 1571-1630) established the following formula to calculate an approximate value V of the volume of a barrel:
Barrel Volume =(πh/12) x (2D2 + d2)
h: height
D: middle radius
d: top & bottom radius
The area A of a torus of radius R generated by a disk of radius r is given by:
A = 4π2 . R . r
in which :
R: large radius
r: small radius
The volume V of a torus of radius R generated by a disk of radius r is given by:
V = 2π2 . r2 . R
in which :
R: large radius
r: small radius