The complying with is a list of volume tasiilaq.nets because that several common shapes. Please to fill in the matching fields and click the "Calculate" button.

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Sphere Volume

Radius (r)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

Cone Volume

Base Radius (r)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Height (h)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

Cube Volume

Edge length (a)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

Cylinder Volume

Base Radius (r)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Height (h)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

Rectangular Tank Volume

Length (l)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Width (w)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Height (h)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

Capsule Volume

Base Radius (r)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Height (h)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

Spherical lid Volume

Please administer any two values below to calculate.

Base Radius (r)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Ball Radius (R)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Height (h)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

Conical Frustum Volume

Top Radius (r)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Bottom Radius (R)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Height (h)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

Ellipsoid Volume

Axis 1 (a)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Axis 2 (b)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Axis 3 (c)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

Square Pyramid Volume

Base edge (a)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Height (h)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

Tube Volume

Outer Diameter (d1)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Inner Diameter (d2)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms
Length (l)milesyardsfeetincheskilometersmeterscentimetersmillimetersmicrometersnanometersangstroms

RelatedSurface Area | Area

Volume is the quantification of the three-dimensional room a problem occupies. The SI unit for volume is the cubic meter, or m3. By convention, the volume the a container is commonly its capacity, and how much fluid it is able come hold, fairly than the amount of room that the yes, really container displaces. Volumes of plenty of shapes deserve to be calculated by making use of well-defined formulas. In part cases, more complicated shapes can be broken down right into simpler accumulation shapes, and also the sum of their quantities is supplied to determine complete volume. The quantities of other even more facility shapes can be calculated making use of integral calculus if a formula exists for the shape"s boundary. Past this, shapes that cannot be defined by recognized equations deserve to be estimated using math methods, such as the finite facet method. Alternatively, if the density of a problem is known, and is uniform, the volume deserve to be calculated using its weight. This computes quantities for few of the most common an easy shapes.

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A ball is the three-dimensional counterpart of a two-dimensional circle. That is a perfectly ring geometrical object that, mathematically, is the collection of points that are equidistant from a given allude at that is center, where the distance between the center and any allude on the ball is the radius r. Likely the most commonly known spherical object is a perfectly ring ball. In ~ mathematics, over there is a difference between a ball and also a sphere, whereby a ball comprises the an are bounded by a sphere. Nevertheless of this distinction, a ball and a round share the same radius, center, and also diameter, and the calculate of their quantities is the same. As with a circle, the longest line segment the connects 2 points of a round through its center is called the diameter, d. The equation because that calculating the volume of a ball is listed below:

volume =4

EX: Claire desires to to fill a perfect spherical water balloon v radius 0.15 ft through vinegar to usage in the water balloon fight versus her arch-nemesis Hilda this comes weekend. The volume that vinegar necessary can be calculated utilizing the equation detailed below:

volume = 4/3 × π × 0.153 = 0.141 ft3


A cone is a three-dimensional shape that tapers smoothly from its typically circular base to a common point called the apex (or vertex). Mathematically, a cone is formed similarly to a circle, through a set of line segments associated to a common center point, other than that the center allude is not included in the plane that contains the one (or some other base). Only the situation of a finite ideal circular cone is thought about on this page. Cones made up of half-lines, non-circular bases, etc. That prolong infinitely will not it is in addressed. The equation for calculating the volume the a cone is as follows:

volume =1

where r is the radius and also h is the elevation of the cone

EX: Bea is identified to walk out of the ice cream cream save with she hard-earned $5 well spent. While she has actually a choice for regular sugar cones, the waffle cones room indisputably larger. She determines the she has a 15% preference for constant sugar cones end waffle cones and also needs to determine whether the potential volume that the waffle cone is ≥ 15% more than that of the street cone. The volume the the waffle cone v a circular base v radius 1.5 in and also height 5 in deserve to be computed using the equation below:

volume = 1/3 × π × 1.52 × 5 = 11.781 in3

Bea also calculates the volume that the street cone and finds the the distinction is 3where a is the edge length of the cube

EX: Bob, that was born in Wyoming (and has actually never left the state), freshly visited his genealogical homeland the Nebraska. Overwhelmed through the magnificence the Nebraska and the atmosphere unlike any type of other he had previously experienced, Bob knew that he had to carry some of Nebraska residence with him. Bob has actually a cubic suitcase v edge lengths of 2 feet, and also calculates the volume that soil that he can lug home v him as follows:

volume = 23 = 8 ft3


A cylinder in its simplest kind is characterized as the surface developed by points at a solved distance native a provided straight line axis. In common use, however, "cylinder" describes a best circular cylinder, where the bases of the cylinder are circles connected through your centers by an axis perpendicular to the plane of that bases, with offered height h and radius r. The equation for calculating the volume that a cylinder is shown below:

volume = πr2h where r is the radius and also h is the elevation of the tank

EX: Caelum desires to construct a sandcastle in the life room the his house. Since he is a firm advocate of recycling, he has recovered three cylindrical barrels indigenous an illegal dumping site and also has cleaned the chemistry waste from the barrels using dishwashing detergent and also water. The barrels each have actually a radius of 3 ft and a elevation of 4 ft, and also Caelum determines the volume of sand that each have the right to hold using the equation below:

volume = π × 32 × 4 = 113.097 ft3

He properly builds a sandcastle in his house, and also as an included bonus, manages come save electricity on night lighting, because his sandcastle glows bright environment-friendly in the dark.

Rectangular Tank

A rectangle-shaped tank is a generalized form of a cube, wherein the sides can have varying lengths. That is bounded by six faces, 3 of which accomplish at the vertices, and all of which space perpendicular to their respective adjacent faces. The equation for calculating the volume of a rectangle is presented below:

volume= size × width × height

EX: Darby likes cake. She goes to the gym for 4 hours a day, every day, come compensate for her love that cake. She plans come hike the Kalalau follow in Kauai and also though incredibly fit, Darby worries around her ability to finish the trail as result of her lack of cake. She decides to fill only the essentials and also wants come stuff her perfectly rectangular load of length, width, and also height 4 ft, 3 ft and 2 ft respectively, with cake. The exact volume of cake she have the right to fit right into her fill is calculated below:

volume = 2 × 3 × 4 = 24 ft3


A capsule is a three-dimensional geometric shape made up of a cylinder and two hemispherical ends, where a hemisphere is half a sphere. It adheres to that the volume that a capsule have the right to be calculated by combining the volume equations for a sphere and a right circular cylinder:

volume = πr2h +4
πr3 = πr2(4
r + h)

where r is the radius and h is the height of the cylindrical portion

EX: provided a capsule with a radius the 1.5 ft and a height of 3 ft, identify the volume of melted milk chocolate m&m"s that Joe can lug in the time capsule he wants to ask for future generations on his trip of self-discovery through the Himalayas:

volume = π × 1.52 × 3 + 4/3 ×π ×1.53 = 35.343 ft3

Spherical Cap

A spherical lid is a part of a round that is separated from the remainder of the sphere by a plane. If the aircraft passes v the facility of the sphere, the spherical lid is referred to as a hemisphere. Various other distinctions exist, including a spherical segment, whereby a round is segmented with two parallel planes and two various radii wherein the airplane pass v the sphere. The equation because that calculating the volume that a spherical cap is acquired from that of a spherical segment, whereby the 2nd radius is 0. In recommendation to the spherical cap presented in the

volume =1
πh2(3R - h)

Given 2 values, the listed computes the 3rd value and also the volume. The equations because that converting between the height and the radii are displayed below:

Given r and R:h = R ± √R2 - r2
Given r and also h:R =h2 + r2
Given R and h: r = √2Rh - h2where r is the radius the the base, R is the radius the the sphere, and h is the height of the spherical cap

EX: Jack really desires to win his girlfriend James in a video game of golf to admire Jill, and also rather than practicing, the decides to sabotage James" golf ball. He cut off a perfect spherical cap from the optimal of James" golf ball, and also needs to calculate the volume of the material crucial to change the spherical cap and skew the weight of James" golf ball. Offered James" golf ball has actually a radius the 1.68 inches, and also the height of the spherical cap the Jack reduced off is 0.3 inches, the volume have the right to be calculated together follows:

volume = 1/3 × π × 0.32 (3 × 1.68 - 0.3) = 0.447 in3

Unfortunately for Jack, James happened to obtain a brand-new shipment that balls the day before their game, and every one of Jack"s efforts were in vain.

Conical Frustum

A conical frustum is the portion of a solid the remains once a cone is cut by two parallel planes. This calculates the volume because that a appropriate circular cone specifically. Common conical frustums discovered in everyday life include lampshades, buckets, and some drink glasses. The volume that a right conical frustum is calculated using the following equation:

volume =1
πh(r2 + rR + R2)

where r and also R are the radii of the bases, h is the elevation of the frustum

EX: Bea has efficiently acquired part ice cream in a sugar cone, and also has just eaten it in a method that leaves the ice cream packed within the cone, and also the ice cream surface level and also parallel to the aircraft of the cone"s opening. She is around to begin eating she cone and also the staying ice cream once her brother grabs her cone and also bites off a ar of the bottom of her cone the is perfectly parallel come the formerly sole opening. Bea is now left through a best conical frustum leaking ice cream cream, and also has to calculation the volume of ice cream cream she must quickly consume given a frustum height of 4 inches, v radii 1.5 inches and also 0.2 inches:

volume=1/3 × π × 4(0.22 + 0.2 × 1.5 + 1.52) = 10.849 in3


An ellipsoid is the three-dimensional counterpart of an ellipse, and is a surface ar that have the right to be defined as the deformation of a round through scaling the directional elements. The facility of one ellipsoid is the point at which 3 pairwise perpendicular axes of symmetry intersect, and also the heat segments delimiting this axes of symmetry are dubbed the principal axes. If all 3 have various lengths, the ellipsoid is commonly described as tri-axial. The equation because that calculating the volume of one ellipsoid is together follows:

volume =4

where a, b, and c space the lengths that the axes

EX: Xabat just likes eat meat, yet his mom insists that he consumes too much, and also only enables him to eat as lot meat together he deserve to fit within an ellipsoid shame bun. Together such, Xabat hollows the end the bun come maximize the volume the meat that he can fit in his sandwich. Offered that his bun has actually axis lengths of 1.5 inches, 2 inches, and also 5 inches, Xabat calculates the volume of meat he can fit in each hollowed bun as follows:

volume = 4/3 × π × 1.5 × 2 × 5 = 62.832 in3

Square Pyramid

A pyramid in geometry is a three-dimensional solid created by connecting a polygonal basic to a suggest called that is apex, wherein a polygon is a form in a airplane bounded by a finite number of straight heat segments. There space many feasible polygonal bases for a pyramid, however a square pyramid is a pyramid in i m sorry the basic is a square. Another difference involving pyramids involves the ar of the apex. A ideal pyramid has actually an apex that is directly over the centroid that its base. Regardless of where the apex that the pyramid is, as long as its elevation is measured together the perpendicular distance from the plane containing the base to that apex, the volume of the pyramid deserve to be composed as: