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VOOZH | about |
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VOOZH | about |
Volume of the shape means the capacity of the shape in three-dimensional space.
Formulas used to calculate the volume of various figures is shown in the image added below:
👁 Volume-FormulasVolume formulas of different solids are given below:
A cube is a 3-D shape in which all its dimensions are equal. (i.e. l = b =h). Rubik's cube is a very common example of a cube. A cube of side 'a' is shown in the image below:
👁 Volume of CubeVolume of the cube formula is given by:
Volume of Cube = a3
where,
A cubiod is a 3-D shape in which all its dimensions are different or may be any two are equal. Matchbox is a very common example of cubiod. A cuboid of length 'l', breadth 'b', and height 'h' is shown in the image below:
👁 Volume of CuboidVolume of cuboid formula is given by:
Volume of Cuboid = lbh
where,
Cylinder is a 3-D which have two flat surfaces and a curved surface. Various example of cylinder are, water tankers, pipes, gas cylinders, etc. A cylinder of height 'h' and radius 'r' is shown in the image below:
👁 Volume of CylinderVolume of cylinder formula is given by:
Volume of Cylinder = πr2h
where,
A sphere is a three-dimensional geometric object that is perfectly round in shape, much like a ball. It is defined as the set of all points in three-dimensional space that are equidistant from a fixed point called the center. A sphere of radius 'r' is shown in the image below:
👁 Volume of SphereVolume of sphere formula is given by:
Volume of Sphere = (4 /3)πr3
where,
A hemisphere is a three-dimensional geometric shape that is half of a sphere. It is formed by slicing a sphere into two equal parts along a plane passing through its center. A hemisphere of radius 'r' is shown in the image below:
👁 Volume of HemisphereVolume of hemisphere formula is given by:
Volume of Hemisphere = (2 /3)πr3
where,
A cone is a three-dimensional geometric shape that tapers smoothly from a flat, circular base to a single point called the apex or vertex. It resembles a party hat or an ice cream cone. A cone of height 'h' and radius 'r' is shown in the image below:
👁 Volume of ConeVolume of cone formula is given by:
Volume of Cone = (1/3)πr2 h
where,
Pyramid is a three-dimensional geometric shape wich has polygonal base and triangular faces that meet at a common point called the apex. A prramid of height 'h' is shown in the image added below:
👁 PyramidFormula for the volume of a pyramid is given as follows,
Volume of Pyramid(V) = 1/3 × Base Area × Height
V = 1/3 A.H cubic units
where,
Volume formulas for various figure are added in the table below:
| Shape | Volume Formulas |
|---|---|
| Cube | a3 |
| Cuboid | l × b × h |
| Cone | (1/3)πr2h |
| Sphere | (4/3)πr3 |
| Hemisphere | (2/3)πr3 |
| Cylinder | πr2h |
| Prism | B × h |
| Pyramid | (1/3) (Bh) |
Volume of any 3-d shape is the space occupied by that shape and is calculated in unit3. The standard unit to measure the side of any 3-d shape is 'm' and so the volume of any 3-d shape is calculated in m3. Other units in which voluemof 3-d shapes is calculated is added in the table below:
| Unit of Side | Unit of Volume | Metric Equivalent |
|---|---|---|
| Inch | Cubic Inches (in3) | 1 cu.in = 16.387064 ml |
| Foot | Cubic Feet (ft3) | 1 cu.ft = 28.316846592 l |
| cm | Cubic centimeter (cm3) | 1 cubic centimeter = 1 ml |
Now some times we came across scenarios in which general unit of volume are used and to convert these general unit of volume to standard unit of volume one must go through the table added below:
| Unit | Conversion |
|---|---|
| 1 Pint (pt) | 2 cups |
| 1 Quart (qt) | 2 pt |
| 1 Gallon (gal) | 3.78 liters |
| 1 liter | 1000 cubic centimeter = 1000 ml |
To calculate volume of any 3-d shapes follow the steps added below:
Step 1: Firstly, identify the shape.
Step 2: Apply the volume formula of the identified shape. If it is a complex shape divide the same into smaller general shape and yhen apply the volume formula to each dhape.
Step 3: Simplify the result and add all the volume of smaller shapes if required. Resultant value gives the volume of the given shape.
Step 4: Use appropriate cubic uniut in the answer to give the exact volume of given shape.
Using these steps one can easily found the volumeof the cube as shown in the examples added below:
Related:
Example 1: Find the volume of cube with side 5 units.
Solution:
Volume of cube is given by:
Volume of Cube = a3
V = 53
Volume of Cube = 125 cubic units
Example 2: Find the volume of cuboid with length, breadth and height as 9, 6 and 5 respectively.
Solution:
Volume of cuboid is given by:
Volume of Cuboid = lbh
V = 9 × 6 × 5
Volume of Cuboid = 270 cubic units
Example 3: Find the volume of cylinder with height 10 units and radius 5 units.
Solution:
Volume of cylinder is given by:
Volume of Cylinder = πr2h
V = π(5)2 × 10
Volume of Cylinder = 250π cubic units
Example 4: Find the volume of cone with height and radius as 13 and 6 units respectively.
Solution:
Volume of cone is given by:
Volume of Cone = (1 /3)πr2h
V = (1 /3)π 62 × 13
V = 12 × 13π
Volume of Cone = 156π cubic units
Example 5: Find the volume of sphere whose radius is 9 units.
Solution:
Volume of sphere is given by:
Volume of Sphere = (4 / 3)πr3
V = (4 / 3)π 93
V = 4 × 243 × π
Volume of Sphere = 972π cubic units
Example 6: Find the volume of hemisphere whose radius is 6 units.
Solution:
Volume of hemisphere is given by:
Volume of Hemisphere = (2/3)πr3
V = (2 / 3)π 63
V = 4 × 36π
Volume of Hemisphere = 144π cubic units
Q1. Find the volume of cube with side 13 units.
Q2. Find the volume of cuboid with length, breadth and height as 19, 8 and 11 respectively.
Q3. Find the volume of cylinder with height 11 units and radius 7 units.
Q4. Find the volume of cone with height and radius as 15 and 12 units respectively.
Q5. Find the volume of sphere whose radius is 4 units.
Q6. Find the volume of hemisphere whose radius is 7 units.
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