what is the volume of the sphere given below? if necessary, round your answer to two decimal places.
Volume Estimator
The following is a listing of book calculators for several common shapes. Please fill up in the respective fields and click the "Calculate" button.
Sphere Book Reckoner
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Cone Volume Calculator
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Cube Volume Computer
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Cylinder Volume Calculator
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Rectangular Tank Book Calculator
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Sheathing Volume Computer
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Spherical Cap Volume Calculator
Please provide whatever two values below to calculate.
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Conical Frustum Volume Figurer
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Ellipsoid Volume Figurer
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Square Pyramid Book Figurer
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Tube Volume Calculator
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Volume is the quantification of the three-dimensional space a substance occupies. The SI unit for book is the cubic meter, or mthree . By convention, the volume of a container is typically its capacity, and how much fluid it is able to hold, rather than the amount of space that the bodily container displaces. Volumes of many shapes can be calculated past using well-defined formulas. In some cases, more complicated shapes can exist broken downwards into simpler aggregate shapes, and the sum of their volumes is used to determine total volume. The volumes of other even more complicated shapes can exist calculated using integral calculus if a formula exists for the shape's boundary. Beyond this, shapes that cannot be described by known equations can exist estimated using mathematical methods, such as the finite element method. Alternatively, if the density of a substance is known, and is compatible, the volume tin can be calculated using its weight. This calculator computes volumes for some of the most common simple shapes.
Sphere
A sphere is the three-dimensional analogue of a ii-dimensional circumvolve. It is a perfectly round geometrical object that, mathematically, is the gear up of points that are equidistant from a given point at its middle, where the distance between the center and any point on the sphere is the radius r. Likely the most commonly known spherical object is a perfectly round ball. Within mathematics, at that place is a distinction between a ball and a sphere, where a ball comprises the space bounded by a sphere. Regardless of this distinction, a ball and a sphere share the same radius, center, and diameter, and the calculation of their volumes is the same. Equally with a circle, the longest line segment that connects two points of a sphere through its heart is called the diameter, d. The equation for calculating the volume of a sphere is provided beneath:
EX: Claire wants to fill up a perfectly spherical h2o balloon with radius 0.15 ft with vinegar to employ in the water airship fight against her arch-nemesis Hilda this coming weekend. The volume of vinegar necessary tin be calculated using the equation provided beneath:
volume = 4/3 × π × 0.fifteeniii = 0.141 ft3
Cone
A cone is a three-dimensional shape that tapers smoothly from its typically round base to a common point called the apex (or vertex). Mathematically, a cone is formed similarly to a circle, by a ready of line segments continued to a mutual center point, except that the middle point is not included in the aeroplane that contains the circumvolve (or some other base). Simply the example of a finite right circular cone is considered on this page. Cones comprised of half-lines, not-circular bases, etc. that extend infinitely will not be addressed. The equation for calculating the volume of a cone is as follows:
where r is the radius and h is the height of the cone
EX: Bea is adamant to walk out of the ice cream store with her hard-earned $five well spent. While she has a preference for regular sugar cones, the waffle cones are indisputably larger. She determines that she has a 15% preference for regular sugar cones over waffle cones and needs to determine whether the potential volume of the waffle cone is ≥ 15% more than that of the sugar cone. The volume of the waffle cone with a circular base with radius ane.5 in and top 5 in tin be computed using the equation beneath:
volume = 1/3 × π × 1.vtwo × v = eleven.781 inthree
Bea also calculates the book of the saccharide cone and finds that the departure is < 15%, and decides to purchase a sugar cone. At present all she has to do is use her angelic, artless appeal to dispense the staff into emptying the containers of ice foam into her cone.
Cube
A cube is the three-dimensional analog of a square, and is an object bounded by half-dozen square faces, three of which meet at each of its vertices, and all of which are perpendicular to their respective next faces. The cube is a special instance of many classifications of shapes in geometry, including being a square parallelepiped, an equilateral cuboid, and a right rhombohedron. Below is the equation for calculating the volume of a cube:
book = a3
where a is the border length of the cube
EX: Bob, who was built-in in Wyoming (and has never left the state), recently visited his ancestral homeland of Nebraska. Overwhelmed by the magnificence of Nebraska and the environment unlike any other he had previously experienced, Bob knew that he had to bring some of Nebraska habitation with him. Bob has a cubic suitcase with border lengths of ii anxiety, and calculates the volume of soil that he tin can bear habitation with him as follows:
volume = 23 = 8 ft3
Cylinder
A cylinder in its simplest form is defined as the surface formed by points at a fixed distance from a given straight line axis. In common use, however, "cylinder" refers to a right circular cylinder, where the bases of the cylinder are circles connected through their centers past an axis perpendicular to the planes of its bases, with given pinnacle h and radius r. The equation for calculating the volume of a cylinder is shown below:
volume = πr2h
where r is the radius and h is the height of the tank
EX: Caelum wants to build a sandcastle in the living room of his house. Because he is a firm abet of recycling, he has recovered three cylindrical barrels from an illegal dumping site and has cleaned the chemical waste material from the barrels using dishwashing detergent and water. The barrels each have a radius of 3 ft and a pinnacle of 4 ft, and Caelum determines the volume of sand that each can agree using the equation below:
volume = π × 3ii × 4 = 113.097 ftthree
He successfully builds a sandcastle in his business firm, and as an added bonus, manages to salvage electricity on dark lighting, since his sandcastle glows bright green in the dark.
Rectangular Tank
A rectangular tank is a generalized form of a cube, where the sides tin can take varying lengths. It is divisional by six faces, 3 of which run across at its vertices, and all of which are perpendicular to their respective adjacent faces. The equation for calculating the volume of a rectangle is shown below:
volume= length × width × height
EX: Darby likes block. She goes to the gym for four hours a day, every twenty-four hour period, to recoup for her love of block. She plans to hike the Kalalau Trail in Kauai and though extremely fit, Darby worries about her ability to complete the trail due to her lack of cake. She decides to pack merely the essentials and wants to stuff her perfectly rectangular pack of length, width, and height iv ft, iii ft and 2 ft respectively, with block. The exact book of cake she can fit into her pack is calculated below:
volume = 2 × 3 × 4 = 24 ft3
Capsule
A capsule is a three-dimensional geometric shape comprised of a cylinder and two hemispherical ends, where a hemisphere is half a sphere. It follows that the volume of a capsule can be calculated by combining the book equations for a sphere and a right round cylinder:
| volume = πr2h + | πr3 = πrii( | r + h) |
where r is the radius and h is the height of the cylindrical portion
EX: Given a capsule with a radius of 1.5 ft and a height of iii ft, determine the volume of melted milk chocolate grand&m's that Joe can carry in the fourth dimension capsule he wants to bury for future generations on his journey of self-discovery through the Himalayas:
volume = π × one.five2 × 3 + 4/3 ×π ×ane.five3 = 35.343 ft3
Spherical Cap
A spherical cap is a portion of a sphere that is separated from the residue of the sphere by a aeroplane. If the plane passes through the centre of the sphere, the spherical cap is referred to as a hemisphere. Other distinctions exist, including a spherical segment, where a sphere is segmented with two parallel planes and ii different radii where the planes pass through the sphere. The equation for calculating the volume of a spherical cap is derived from that of a spherical segment, where the 2nd radius is 0. In reference to the spherical cap shown in the calculator:
Given two values, the calculator provided computes the third value and the volume. The equations for converting betwixt the height and the radii are shown below:
Given r and R: h = R ± √R2 - rii
Given R and h: r = √2Rh - h2
where r is the radius of the base, R is the radius of the sphere, and h is the height of the spherical cap
EX: Jack really wants to crush his friend James in a game of golf game to impress Jill, and rather than practicing, he decides to sabotage James' golf game brawl. He cuts off a perfect spherical cap from the tiptop of James' golf brawl, and needs to calculate the volume of the material necessary to replace the spherical cap and skew the weight of James' golf ball. Given James' golf ball has a radius of 1.68 inches, and the height of the spherical cap that Jack cutting off is 0.3 inches, the volume can be calculated as follows:
book = 1/3 × π × 0.iii2 (three × 1.68 - 0.iii) = 0.447 in3
Unfortunately for Jack, James happened to receive a new shipment of assurance the day before their game, and all of Jack'southward efforts were in vain.
Conical Frustum
A conical frustum is the portion of a solid that remains when a cone is cut by 2 parallel planes. This reckoner calculates the volume for a right circular cone specifically. Typical conical frustums plant in everyday life include lampshades, buckets, and some drinking glasses. The book of a right conical frustum is calculated using the following equation:
| book = | πh(rtwo + rR + R2) |
where r and R are the radii of the bases, h is the peak of the frustum
EX: Bea has successfully acquired some water ice cream in a sugar cone, and has merely eaten it in a fashion that leaves the ice foam packed inside the cone, and the ice foam surface level and parallel to the plane of the cone's opening. She is virtually to start eating her cone and the remaining ice cream when her brother grabs her cone and bites off a section of the bottom of her cone that is perfectly parallel to the previously sole opening. Bea is now left with a right conical frustum leaking ice cream, and has to summate the volume of ice foam she must quickly swallow given a frustum height of iv inches, with radii 1.5 inches and 0.ii inches:
volume=one/iii × π × 4(0.2ii + 0.two × ane.v + 1.52) = 10.849 in3
Ellipsoid
An ellipsoid is the three-dimensional counterpart of an ellipse, and is a surface that tin be described equally the deformation of a sphere through scaling of directional elements. The center of an ellipsoid is the betoken at which iii pairwise perpendicular axes of symmetry intersect, and the line segments delimiting these axes of symmetry are chosen the master axes. If all three have different lengths, the ellipsoid is commonly described equally tri-axial. The equation for calculating the volume of an ellipsoid is as follows:
where a, b, and c are the lengths of the axes
EX: Xabat just likes eating meat, but his mother insists that he consumes likewise much, and merely allows him to swallow as much meat as he can fit within an ellipsoid shaped bun. Equally such, Xabat hollows out the bun to maximize the volume of meat that he can fit in his sandwich. Given that his bun has axis lengths of 1.v inches, 2 inches, and 5 inches, Xabat calculates the book of meat he can fit in each hollowed bun equally follows:
volume = iv/3 × π × 1.five × 2 × 5 = 62.832 in3
Square Pyramid
A pyramid in geometry is a iii-dimensional solid formed by connecting a polygonal base to a point called its apex, where a polygon is a shape in a plane bounded by a finite number of directly line segments. In that location are many possible polygonal bases for a pyramid, but a square pyramid is a pyramid in which the base of operations is a square. Some other distinction involving pyramids involves the location of the apex. A correct pyramid has an noon that is straight higher up the centroid of its base of operations. Regardless of where the noon of the pyramid is, as long as its tiptop is measured as the perpendicular distance from the aeroplane containing the base of operations to its noon, the volume of the pyramid tin can be written as:
Generalized pyramid volume:
where b is the expanse of the base and h is the height
Square pyramid book:
where a is the length of the base of operations'due south border
EX: Wan is fascinated by ancient Arab republic of egypt and specially enjoys anything related to the pyramids. Being the eldest of his siblings As well, Tree and Fore, he is able to hands corral and deploy them at his will. Taking reward of this, Wan decides to re-enact ancient Egyptian times and have his siblings act as workers edifice him a pyramid of mud with edge length 5 anxiety and pinnacle 12 anxiety, the book of which can be calculated using the equation for a square pyramid:
volume = 1/3 × fivetwo × 12 = 100 ft3
Tube Pyramid
A tube, frequently also referred to as a piping, is a hollow cylinder that is often used to transfer fluids or gas. Computing the book of a tube essentially involves the aforementioned formula as a cylinder (volume=prtwoh), except that in this case, the diameter is used rather than the radius, and length is used rather than height. The formula, therefore, involves measuring the diameters of the inner and outer cylinder, as shown in the figure to a higher place, calculating each of their volumes, and subtracting the volume of the inner cylinder from that of the outer 1. Considering the use of length and diameter mentioned above, the formula for calculating the volume of a tube is shown below:
where d1 is the outer bore, d2 is the inner diameter, and l is the length of the tube
EX: Beulah is dedicated to environmental conservation. Her construction company uses but the most environmentally friendly of materials. She also prides herself on meeting client needs. One of her customers has a holiday home built in the forest, across a creek. He wants easier admission to his house, and requests that Beulah build him a route, while ensuring that the creek can flow freely and so as not to disrupt his favorite fishing spot. She decides that the pesky beaver dams would exist a proficient point to build a pipage through the creek. The volume of patented depression-touch concrete required to build a piping of outer diameter iii feet, inner diameter 2.v feet, and length of ten anxiety, tin be calculated as follows:
| volume = π × | × l0 = 21.6 ftthree |
Common Book Units
| Unit | cubic meters | milliliters |
| milliliter (cubic centimeter) | 0.000001 | 1 |
| cubic inch | 0.00001639 | sixteen.39 |
| pint | 0.000473 | 473 |
| quart | 0.000946 | 946 |
| liter | 0.001 | ane,000 |
| gallon | 0.003785 | three,785 |
| cubic foot | 0.028317 | 28,317 |
| cubic g | 0.764555 | 764,555 |
| cubic meter | 1 | 1,000,000 |
| cubic kilometer | 1,000,000,000 | 10fifteen |
Source: https://www.calculator.net/volume-calculator.html
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