what is the volume of the sphere round the answer to the nearest cubic unit
Volume Calculator
The post-obit is a list of volume calculators for several common shapes. Please make full in the respective fields and click the "Calculate" button.
Sphere Volume Calculator
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Cone Volume Calculator
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Cube Volume Figurer
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Cylinder Volume Calculator
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Rectangular Tank Book Estimator
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Capsule Volume Calculator
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Spherical Cap Volume Calculator
Please provide whatever ii values below to calculate.
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Conical Frustum Volume Calculator
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Ellipsoid Volume Estimator
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Square Pyramid Volume Calculator
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Tube Volume Estimator
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Volume is the quantification of the three-dimensional infinite a substance occupies. The SI unit for volume is the cubic meter, or 10003 . By convention, the volume of a container is typically its capacity, and how much fluid it is able to concord, rather than the amount of infinite that the bodily container displaces. Volumes of many shapes tin can be calculated by using well-divers formulas. In some cases, more complicated shapes can exist broken down into simpler aggregate shapes, and the sum of their volumes is used to decide total volume. The volumes of other even more complicated shapes can be calculated using integral calculus if a formula exists for the shape's purlieus. Beyond this, shapes that cannot be described by known equations can be estimated using mathematical methods, such as the finite chemical element method. Alternatively, if the density of a substance is known, and is uniform, the book can be calculated using its weight. This calculator computes volumes for some of the most common elementary shapes.
Sphere
A sphere is the iii-dimensional counterpart of a 2-dimensional circle. It is a perfectly round geometrical object that, mathematically, is the gear up of points that are equidistant from a given point at its center, where the altitude betwixt the heart and whatsoever point on the sphere is the radius r. Probable the most ordinarily known spherical object is a perfectly round ball. Inside mathematics, at that place is a distinction between a brawl and a sphere, where a ball comprises the space bounded by a sphere. Regardless of this stardom, a ball and a sphere share the same radius, heart, and diameter, and the calculation of their volumes is the same. As with a circle, the longest line segment that connects two points of a sphere through its center is called the diameter, d. The equation for computing the volume of a sphere is provided below:
EX: Claire wants to fill up a perfectly spherical water balloon with radius 0.fifteen ft with vinegar to use in the water balloon fight against her arch-nemesis Hilda this coming weekend. The book of vinegar necessary can exist calculated using the equation provided below:
volume = iv/3 × π × 0.153 = 0.141 ft3
Cone
A cone is a 3-dimensional shape that tapers smoothly from its typically circular base of operations to a common point called the apex (or vertex). Mathematically, a cone is formed similarly to a circle, by a prepare of line segments connected to a mutual center point, except that the center point is not included in the airplane that contains the circumvolve (or some other base). Only the case of a finite right circular cone is considered on this page. Cones comprised of half-lines, non-round bases, etc. that extend infinitely will not exist 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 determined to walk out of the ice cream store with her hard-earned $5 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 saccharide cones over waffle cones and needs to determine whether the potential book of the waffle cone is ≥ fifteen% more than that of the sugar cone. The volume of the waffle cone with a round base with radius 1.5 in and height 5 in can exist computed using the equation beneath:
book = 1/3 × π × 1.52 × five = eleven.781 in3
Bea also calculates the volume of the sugar cone and finds that the divergence is < 15%, and decides to purchase a sugar cone. Now all she has to exercise is use her angelic, artless appeal to manipulate the staff into emptying the containers of ice cream into her cone.
Cube
A cube is the 3-dimensional analog of a square, and is an object bounded by six square faces, three of which run across at each of its vertices, and all of which are perpendicular to their corresponding adjacent faces. The cube is a special case 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:
volume = a3
where a is the border length of the cube
EX: Bob, who was born in Wyoming (and has never left the state), recently visited his ancestral homeland of Nebraska. Overwhelmed by the magnificence of Nebraska and the environment different any other he had previously experienced, Bob knew that he had to bring some of Nebraska domicile with him. Bob has a cubic suitcase with edge lengths of 2 anxiety, and calculates the book of soil that he tin can carry home with him as follows:
volume = 23 = 8 ft3
Cylinder
A cylinder in its simplest form is defined equally the surface formed past points at a fixed distance from a given straight line centrality. In mutual apply, withal, "cylinder" refers to a correct circular cylinder, where the bases of the cylinder are circles connected through their centers by an axis perpendicular to the planes of its bases, with given superlative h and radius r. The equation for calculating the book of a cylinder is shown below:
volume = πrtwoh
where r is the radius and h is the acme of the tank
EX: Caelum wants to build a sandcastle in the living room of his house. Because he is a business firm abet of recycling, he has recovered three cylindrical barrels from an illegal dumping site and has cleaned the chemic waste from the barrels using dishwashing detergent and water. The barrels each have a radius of 3 ft and a acme 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 house, and as an added bonus, manages to save electricity on nighttime lighting, since his sandcastle glows bright light-green in the dark.
Rectangular Tank
A rectangular tank is a generalized class of a cube, where the sides tin accept varying lengths. Information technology is bounded by six faces, 3 of which meet at its vertices, and all of which are perpendicular to their respective adjacent faces. The equation for computing the book of a rectangle is shown beneath:
book= length × width × height
EX: Darby likes cake. She goes to the gym for four hours a twenty-four hours, every day, to compensate for her love of cake. She plans to hike the Kalalau Trail in Kauai and though extremely fit, Darby worries about her power to complete the trail due to her lack of cake. She decides to pack just the essentials and wants to stuff her perfectly rectangular pack of length, width, and height four ft, iii ft and 2 ft respectively, with cake. The exact volume of cake she can fit into her pack is calculated below:
volume = two × 3 × 4 = 24 ft3
Capsule
A capsule is a three-dimensional geometric shape comprised of a cylinder and 2 hemispherical ends, where a hemisphere is half a sphere. Information technology follows that the volume of a capsule can be calculated by combining the volume equations for a sphere and a right round cylinder:
| volume = πr2h + | πr3 = πr2( | r + h) |
where r is the radius and h is the acme of the cylindrical portion
EX: Given a capsule with a radius of one.v ft and a summit of 3 ft, determine the book of melted milk chocolate grand&yard's that Joe can carry in the time sheathing he wants to bury for future generations on his journey of self-discovery through the Himalayas:
volume = π × 1.52 × 3 + 4/3 ×π ×ane.53 = 35.343 ft3
Spherical Cap
A spherical cap is a portion of a sphere that is separated from the residue of the sphere past a plane. If the plane passes through the center of the sphere, the spherical cap is referred to as a hemisphere. Other distinctions be, including a spherical segment, where a sphere is segmented with 2 parallel planes and two 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 second radius is 0. In reference to the spherical cap shown in the calculator:
Given 2 values, the calculator provided computes the tertiary value and the volume. The equations for converting between 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 beat his friend James in a game of golf to impress Jill, and rather than practicing, he decides to sabotage James' golf ball. He cuts off a perfect spherical cap from the top of James' golf ball, and needs to calculate the volume of the textile necessary to replace the spherical cap and skew the weight of James' golf brawl. Given James' golf brawl has a radius of i.68 inches, and the top of the spherical cap that Jack cut off is 0.3 inches, the volume can be calculated as follows:
volume = 1/3 × π × 0.3two (3 × 1.68 - 0.3) = 0.447 in3
Unfortunately for Jack, James happened to receive a new shipment of balls the day before their game, and all of Jack'due south 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 figurer calculates the volume for a correct circular cone specifically. Typical conical frustums found in everyday life include lampshades, buckets, and some drinking glasses. The book of a right conical frustum is calculated using the following equation:
| volume = | πh(rtwo + rR + R2) |
where r and R are the radii of the bases, h is the height of the frustum
EX: Bea has successfully acquired some ice cream in a sugar cone, and has only eaten it in a fashion that leaves the ice cream packed inside the cone, and the water ice cream surface level and parallel to the aeroplane of the cone'south opening. She is about to start eating her cone and the remaining water ice cream when her brother grabs her cone and bites off a section of the lesser of her cone that is perfectly parallel to the previously sole opening. Bea is at present left with a right conical frustum leaking water ice cream, and has to calculate the volume of ice cream she must quickly eat given a frustum height of 4 inches, with radii 1.five inches and 0.2 inches:
volume=1/3 × π × 4(0.twoii + 0.ii × 1.v + i.5two) = ten.849 iniii
Ellipsoid
An ellipsoid is the iii-dimensional counterpart of an ellipse, and is a surface that tin can be described as the deformation of a sphere through scaling of directional elements. The center of an ellipsoid is the signal at which three pairwise perpendicular axes of symmetry intersect, and the line segments delimiting these axes of symmetry are called the primary axes. If all three have different lengths, the ellipsoid is commonly described every bit tri-axial. The equation for computing the volume of an ellipsoid is as follows:
where a, b, and c are the lengths of the axes
EX: Xabat only likes eating meat, but his mother insists that he consumes too much, and only allows him to swallow as much meat as he tin can fit within an ellipsoid shaped bun. Every bit such, Xabat hollows out the bun to maximize the book of meat that he can fit in his sandwich. Given that his bun has axis lengths of 1.5 inches, 2 inches, and 5 inches, Xabat calculates the volume of meat he can fit in each hollowed bun as follows:
volume = 4/3 × π × i.5 × 2 × 5 = 62.832 in3
Square Pyramid
A pyramid in geometry is a three-dimensional solid formed by connecting a polygonal base to a bespeak called its apex, where a polygon is a shape in a airplane divisional by a finite number of straight line segments. There are many possible polygonal bases for a pyramid, simply a square pyramid is a pyramid in which the base is a square. Another distinction involving pyramids involves the location of the apex. A right pyramid has an apex that is directly above the centroid of its base. Regardless of where the apex of the pyramid is, as long as its height is measured as the perpendicular altitude from the plane containing the base to its apex, the book of the pyramid can be written equally:
Generalized pyramid volume:
where b is the area of the base and h is the height
Foursquare pyramid volume:
where a is the length of the base's edge
EX: Wan is fascinated by ancient Arab republic of egypt and specially enjoys anything related to the pyramids. Being the eldest of his siblings Too, Tree and Fore, he is able to easily corral and deploy them at his will. Taking advantage of this, Wan decides to re-enact aboriginal Egyptian times and have his siblings act as workers building him a pyramid of mud with edge length 5 feet and height 12 anxiety, the book of which can be calculated using the equation for a foursquare pyramid:
volume = 1/iii × 52 × 12 = 100 ft3
Tube Pyramid
A tube, often too referred to every bit a pipe, is a hollow cylinder that is often used to transfer fluids or gas. Computing the volume of a tube essentially involves the same formula as a cylinder (volume=pr2h), except that in this instance, the bore 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 above, calculating each of their volumes, and subtracting the book of the inner cylinder from that of the outer one. Considering the apply of length and bore mentioned in a higher place, the formula for calculating the volume of a tube is shown below:
where d1 is the outer bore, dtwo is the inner diameter, and l is the length of the tube
EX: Beulah is defended to environmental conservation. Her construction company uses merely the most environmentally friendly of materials. She too prides herself on meeting client needs. One of her customers has a vacation home built in the woods, across a creek. He wants easier access to his business firm, and requests that Beulah build him a road, while ensuring that the creek can flow freely and then as not to disrupt his favorite fishing spot. She decides that the pesky beaver dams would be a good point to build a pipe through the creek. The volume of patented low-bear upon concrete required to build a piping of outer diameter 3 feet, inner bore 2.5 feet, and length of 10 anxiety, can be calculated as follows:
| volume = π × | × l0 = 21.6 ftiii |
Mutual Volume Units
| Unit of measurement | cubic meters | milliliters |
| milliliter (cubic centimeter) | 0.000001 | 1 |
| cubic inch | 0.00001639 | 16.39 |
| pint | 0.000473 | 473 |
| quart | 0.000946 | 946 |
| liter | 0.001 | one,000 |
| gallon | 0.003785 | three,785 |
| cubic foot | 0.028317 | 28,317 |
| cubic yard | 0.764555 | 764,555 |
| cubic meter | 1 | 1,000,000 |
| cubic kilometer | i,000,000,000 | xfifteen |
Source: https://www.calculator.net/volume-calculator.html
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