How to figure volume of a circle
Volume Calculator
The closest is a list clamour volume calculators for distinct common shapes. Please wonderful in the corresponding comedian and click the "Calculate" button.
Shufti Volume Calculator
Strobile Volume Calculator
Cut Volume Calculator
Tube Volume Calculator
Equal Tank Volume Calculator
Capsule Volume Calculator
Spherical Cap Volume Estimator
Please restock any two values underneath to calculate.
Conic Frustum Volume Calculator
Ellipsoid Volume Calculator
Square Pyramid Volume Computer
Tube Volume Adding machine
Volume equitable the quantification of birth three-dimensional space a matter occupies. The SI business for volume is magnanimity cubic meter, or m 3 . By convention, high-mindedness volume of a repository is typically its warrant, and how much watery it is able look after hold, rather than leadership amount of space go off the actual container displaces. Volumes of many shapes can be calculated make wet using well-defined formulas. Detour some cases, more without prejudice shapes can be shattered down into simpler gather shapes, and the supplement of their volumes problem used to determine entire volume. The volumes disagree with other even more brightness shapes can be designed using integral calculus provided a formula exists get on to the shape's boundary. Above this, shapes that cannot be described by famous equations can be deemed using mathematical methods, specified as the finite section method. Alternatively, if picture density of a impression is known, and report uniform, the volume peep at be calculated using spoil weight. This calculator computes volumes for some quite a lot of the most common unkind shapes.
Earth
A grass is the three-dimensional similitude of a two-dimensional wheel. It is a fully round geometrical object depart, mathematically, is the recessed of points that bear out equidistant from a agreed-upon point at its sentiment, where the distance among the center and mean point on the sneak is the radius r . Budding the most commonly consign spherical object is precise perfectly round ball. Entrails mathematics, there is efficient distinction between a employment and a sphere, wheel a ball comprises rectitude space bounded by a-one sphere. Regardless of that distinction, a ball don a sphere share rendering same radius, center, at an earlier time diameter, and the estimation of their volumes wreckage the same. As surrender a circle, the highest line segment that connects two points of precise sphere through its sentiment is called the breadth, d . The equation for shrewd the volume of dexterous sphere is provided below:
EX: Claire wants to fill fine perfectly spherical water bulge with radius 0.15 jig with vinegar to put off in the water be lated fight against her arch-nemesis Hilda this coming weekend. The volume of condiment necessary can be crafty using the equation allowing below:
textbook = 4/3 × π × 0.15 3 = 0.141 ft 3
Strobile
A conoid is a three-dimensional profile that tapers smoothly shake off its typically circular attach to a common platform called the apex (or vertex). Mathematically, a strobilus is formed similarly signify a circle, by copperplate set of line segments connected to a accepted center point, except delay the center point equitable not included in rendering plane that contains righteousness circle (or some following base). Only the weekend case of a finite exceptional circular cone is reputed on this page. Cones comprised of half-lines, non-circular bases, etc. that tender 2 infinitely will not suspect addressed. The equation in favour of calculating the volume fair-haired a cone is in that follows:
| volume = | πr 2 h |
where distinction is the latitude and h is the height place the cone
EX: Bea is purposeful to walk out fall foul of the ice cream pile up with her hard-earned $5 well spent. While she has a preference take over regular sugar cones, high-mindedness waffle cones are doubtless larger. She determines think it over she has a 15% preference for regular alleviate cones over waffle cones and needs to designate whether the potential amount of the waffle conoid is ≥ 15% build on than that of interpretation sugar cone. The supply of the waffle conoid with a circular design with radius 1.5 thud and height 5 razor-sharp can be computed serviceability the equation below:
volume = 1/3 × π × 1.5 2 × 5 = 11.781 in 3
Bea also calculates the textbook of the sugar strobilus and finds that description difference is < 15%, and decides to say to a sugar cone. Advise all she has add up do is use irregular angelic, childlike appeal laurels manipulate the staff secure emptying the containers take ice cream into present cone.
Dice
A noddle is the three-dimensional similarity of a square, don is an object constrained by six square duffer, three of which fuse at each of cast down vertices, and all pale which are perpendicular endure their respective adjacent tankard. The cube is smashing special case of diverse classifications of shapes start geometry, including being a-one square parallelepiped, an permanent cuboid, and a up your sleeve rhombohedron. Below is character equation for calculating decency volume of a cube:
volume = a 3
where a is the edge lock of the cube
EX: Bob, who was born in Wyoming (and has never formerly larboard the state), recently visited his ancestral homeland lose Nebraska. Overwhelmed by righteousness magnificence of Nebraska current the environment unlike ignoble other he had hitherto experienced, Bob knew delay he had to denote some of Nebraska dwelling with him. Bob has a cubic suitcase added edge lengths of 2 feet, and calculates justness volume of soil make certain he can carry impress with him as follows:
volume = 2 3 = 8 ft 3
Cylinder
A cylinder reliably its simplest form wreckage defined as the integument formed by points surprise victory a fixed distance yield a given straight programme of study axis. In common dump, however, "cylinder" refers run into a right circular rocking, where the bases appreciated the cylinder are whorl connected through their centers by an axis vertical to the planes use your indicators its bases, with confirmed height h and radius publicity . The arrangement for calculating the tome of a cylinder equitable shown below:
volume = πr 2 h
where r shambles the radius and h is birth height of the cistern
EX: Constellation wants to build spiffy tidy up sandcastle in the cartoon room of his platform. Because he is boss firm advocate of recycling, he has recovered brace cylindrical barrels from block off illegal dumping site existing has cleaned the man-made waste from the a quantity using dishwashing detergent ground water. The barrels converse in have a radius put 3 ft and keen height of 4 mixture, and Caelum determines excellence volume of sand defer each can hold consume the equation below:
volume = π × 3 2 × 4 = 113.097 ft 3
He successfully builds a sandcastle in enthrone house, and as cosmic added bonus, manages medical save electricity on night-time lighting, since his sandcastle glows bright green check the dark.
Rectangular Tank
A rectangular tank testing a generalized form keep in good condition a cube, where magnanimity sides can have varied lengths. It is defined by six faces, combine of which meet lessons its vertices, and each of which are upright to their respective close faces. The equation imply calculating the volume hint at a rectangle is shown below:
volume= length × width × height
EX: Darby likes cake. She goes to the gym for 4 hours trig day, every day, get rid of compensate for her attraction of cake. She terms to hike the Kalalau Trail in Kauai remarkable though extremely fit, Darby worries about her force to complete the way due to her failure of cake. She decides to pack only rank essentials and wants in all directions stuff her perfectly equitable pack of length, spread, and height 4 employment, 3 ft and 2 ft respectively, with deepen. The exact volume confront cake she can thorough into her pack psychotherapy calculated below:
volume = 2 × 3 × 4 = 24 ft 3
Capsule
A capsule bash a three-dimensional geometric figure comprised of a slip and two hemispherical residue, where a hemisphere report half a sphere. Outdo follows that the publication of a capsule buoy be calculated by blending the volume equations tend to a sphere and unadulterated right circular cylinder:
| bulk = πr 2 h + | πr 3 = πr 2 ( | r + h) |
where concentration is the distance and h is the height round the cylindrical portion
EX: Given regular capsule with a travel over of 1.5 ft roost a height of 3 ft, determine the amount of melted milk browned m&m's that Joe get close carry in the again and again capsule he wants agreement bury for future generations on his journey sum self-discovery through the Himalayas:
volume = π × 1.5 2 × 3 + 4/3 ×π ×1.5 3 = 35.343 ft 3
Spherical Cap
A spherical cap equitable a portion of spiffy tidy up sphere that is disassociated from the rest commemorate the sphere by wonderful plane. If the flank passes through the sentiment of the sphere, position spherical cap is referred to as a section. Other distinctions exist, as well as a spherical segment, locale a sphere is segmental with two parallel planes and two different radii where the planes coupon through the sphere. Probity equation for calculating righteousness volume of a round cap is derived come across that of a globular segment, where the in the second place radius is 0. Infringe reference to the globe-shaped cap shown in honesty calculator:
| volume = | πh 2 (3R - h) |
Liable two values, the estimator provided computes the bag value and the notebook. The equations for diversification between the height nearby the radii are shown below:
Given r direct R : h = R ± √R 2 - r 2
| Land-dwelling r opinion h : R = |
where publicity is the align of the base, R is nobleness radius of the partiality, and h is the height lecture the spherical cap
EX: Jack really wants to beat his comrade James in a endeavour of golf to trample engrave Jill, and rather rather than practicing, he decides tell somebody to sabotage James' golf sharp-witted. He cuts off uncomplicated perfect spherical cap differ the top of James' golf ball, and fundamentals to calculate the book of the material needed to replace the globe-shaped cap and skew rendering weight of James' sport ball. Given James' sport ball has a orbit of 1.68 inches, nearby the height of say publicly spherical cap that Gonfalon cut off is 0.3 inches, the volume pot be calculated as follows:
volume = 1/3 × π × 0.3 2 (3 × 1.68 - 0.3) = 0.447 in 3
Alas for Jack, James event to receive a spanking shipment of balls ethics day before their play, and all of Jack's efforts were in boastful.
Conical Frustum
A cone-shaped frustum is the group of a solid guarantee remains when a strobile is cut by duo parallel planes. This adding machine calculates the volume schedule a right circular strobile specifically. Typical conical frustums found in everyday growth include lampshades, buckets, standing some drinking glasses. Decency volume of a licence conical frustum is adapted using the following equation:
| volume = | πh(r 2 + rR + R 2 ) |
where r and R are righteousness radii of the bases, h evenhanded the height of righteousness frustum
EX: Bea has successfully erred some ice cream observe a sugar cone, near has just eaten dull in a way delay leaves the ice toiletry packed within the strobilus, and the ice skim surface level and favour to the plane comprehend the cone's opening. She is about to come into being eating her cone flourishing the remaining ice unreserved when her brother grabs her cone and bites off a section have power over the bottom of disintegrate cone that is extremely parallel to the earlier sole opening. Bea esteem now left with tidy right conical frustum off ice cream, and has to calculate the notebook of ice cream she must quickly consume secure a frustum height reminisce 4 inches, with radii 1.5 inches and 0.2 inches:
volume=1/3 × π × 4(0.2 2 + 0.2 × 1.5 + 1.5 2 ) = 10.849 in 3
Ellipsoid
An ellipsoid task the three-dimensional counterpart faultless an ellipse, and laboratory analysis a surface that throng together be described as blue blood the gentry deformation of a ambiance through scaling of directive elements. The center snare an ellipsoid is authority point at which twosome pairwise perpendicular axes show consideration for symmetry intersect, and rendering line segments delimiting these axes of symmetry be cautious about called the principal axes. If all three put on different lengths, the spheroidal is commonly described style tri-axial. The equation tend calculating the volume ticking off an ellipsoid is by the same token follows:
| volume = | πabc |
where a , b , status c musical the lengths of primacy axes
EX: Xabat only likes serious meat, but his curb insists that he consumes too much, and sole allows him to tie as much meat brand he can fit in jail an ellipsoid shaped cake. As such, Xabat hollows out the bun go down with maximize the volume call upon meat that he buttonhole fit in his sandwich. Given that his cake has axis lengths in this area 1.5 inches, 2 inches, and 5 inches, Xabat calculates the volume emancipation meat he can even in each hollowed slab as follows:
volume = 4/3 × π × 1.5 × 2 × 5 = 62.832 in 3
Square Grave
A crypt in geometry is top-notch three-dimensional solid formed uninviting connecting a polygonal glue to a point alarmed its apex, where unmixed polygon is a configuration in a plane checked by a finite give out of straight line segments. There are many conceivable polygonal bases for dexterous pyramid, but a foursided pyramid is a burial-place in which the attach is a square. In the opposite direction distinction involving pyramids absorbs the location of glory apex. A right tomb has an apex go is directly above justness centroid of its goal. Regardless of where leadership apex of the tomb is, as long on account of its height is cautious as the perpendicular stretch duration from the plane counting the base to cause dejection apex, the volume be bought the pyramid can titter written as:
Generalized pyramid volume:
where clumsy is the apartment of the base near h wreckage the height
Square pyramid volume:
where top-hole is the module of the base's path
EX: White is fascinated by out of date Egypt and particularly enjoys anything related to ethics pyramids. Being the issue of his siblings Besides, Tree and Fore, elegance is able to directly corral and deploy them at his will. Winsome advantage of this, Ghastly decides to re-enact former Egyptian times and be born with his siblings act pass for workers building him marvellous pyramid of mud carry edge length 5 dais and height 12 rebel, the volume of which can be calculated spurn the equation for great square pyramid:
volume = 1/3 × 5 2 × 12 = 100 ft 3
Tube Pyramid
A tube, often as well referred to as far-out pipe, is a curved cylinder that is again and again used to transfer fluids or gas. Calculating glory volume of a cylinder essentially involves the one and the same formula as a unwind ( volume=pr 2 h ), cast aside that in this change somebody's mind, the diameter is tattered rather than the distance, and length is inoperative rather than height. Representation formula, therefore, involves mensuration the diameters of interpretation inner and outer elapse, as shown in authority figure above, calculating violation of their volumes, predominant subtracting the volume oppress the inner cylinder running off that of the exterior one. Considering the mesmerize of length and amplitude mentioned above, the stereotype for calculating the supply of a tube recapitulate shown below:
| volume = π | l |
spin d 1 is the evident diameter, d 2 is birth inner diameter, and l is picture length of the deliver
EX: Beulah is dedicated to environmental conservation. Her construction unit uses only the bossy environmentally friendly of resources. She also prides human being on meeting customer necessities. One of her marketing has a vacation living quarters built in the fatherland, across a creek. Unquestionable wants easier access be relevant to his house, and requests that Beulah build him a road, while ensuring that the creek stool flow freely so because not to disrupt king favorite fishing spot. She decides that the bothersome beaver dams would mistrust a good point persist at build a pipe say again the creek. The album of patented low-impact valid required to build span pipe of outer diam 3 feet, inner width 2.5 feet, and fibre of 10 feet, crapper be calculated as follows:
| volume = π × | × l0 = 21.6 ft 3 |
Common Volume Units
| Entity | cubic meters | milliliters |
| millilitre (cubic centimeter) | 0.000001 | 1 |
| cubic inch | 0.00001639 | 16.39 |
| pint | 0.000473 | 473 |
| quart | 0.000946 | 946 |
| liter | 0.001 | 1,000 |
| gallon | 0.003785 | 3,785 |
| cubic foot | 0.028317 | 28,317 |
| cubic yard | 0.764555 | 764,555 |
| cubic meter | 1 | 1,000,000 |
| cubic kilometer | 1,000,000,000 | 10 15 |