ठोसों के संयोजन का आयतन: Difference between revisions
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The volume of the combination of solids will be equal to the sum of the volume of individual solids. | |||
== Volume of a Combination of solids Formula == | |||
We get the volume of a combination of a solids by adding the volume of the individual solids. Hence, the formula to calculate the volume of a combination of solids is given by the formula, | |||
<math>V=V_1+V_2+.....</math> | |||
Where | |||
<math>V</math>is the volume of the combination of solids | |||
<math>V_1</math> and <math>V_2</math> are the volume of the individual solids such as solid <math>1</math>, solid <math>2</math>, and so on. | |||
== Volume of Solids Formula == | |||
Here are the formula for volumes of all the three-dimensional solid shapes. | |||
For a cuboid which has length <math>l</math>, breadth <math>b</math> and height <math>h</math>, the formula for volume and surface area is given by: | |||
* Volume = <math>l\times b \times h</math> | |||
* Total surface area = <math>2(lb+bh+lh)</math> | |||
* Length of diagonal of cuboid = <math>\sqrt{l^2+b^2+h^2}</math> | |||
For a cube having edge length equal to <math>a</math>, the formula for volume and surface area is given by: | |||
* Volume = <math>a^3</math> | |||
* Total surface area = <math>6a^2</math> | |||
* Length of diagonal of cube = <math>\sqrt3a</math> | |||
Similarly, for other shapes | |||
* Volume of Sphere = <math>\frac{4}{3}\pi r^3</math> | |||
* Volume of Cone = <math>\frac{1}{3}\pi r^2h</math> | |||
* Volume of Cylinder = <math>\pi r^2h</math> | |||
* Volume of Hemisphere =<math>\frac{2}{3}\pi r^3</math> | |||
== Example == | |||
A cylinder of volume <math>150</math> cm<sup>3</sup> is placed with a cone, whose height is <math>4</math> cm. If the height of cone and cylinder is equal, then find the total volume of the shape formed by the combination of cylinder and cone. | |||
'''Solution''': | |||
Given, Volume of cylinder <math>V_1=150</math> cm<sup>3</sup> | |||
Height of cylinder = Height of cone = <math>4</math> cm | |||
The formula for Volume of cylinder is | |||
<math>V_1=\pi r^2h</math> | |||
<math>150=\pi\times r^2 \times 4</math> | |||
<math>r^2 =\frac{150}{4\pi} ........(1)</math> | |||
The formula for Volume of cone is given by: | |||
<math>V_2=\frac{1}{3}\pi r^2h</math> | |||
By putting the value of <math>r^2</math> from eq. <math>(1)</math> | |||
<math>V_2=\frac{1}{3}\pi \times \frac{150}{4\pi} \times 4</math> | |||
<math>V_2=50</math> cm<sup>3</sup> | |||
Therefore, the total volume of the combined solids, <math>V=V_1+V_2=150+50=200</math> cm<sup>3</sup> | |||
'''Note:''' Volume of Cone = <math>\frac{1}{3}</math>(Volume of Cylinder) | |||
[[Category:पृष्ठीय क्षेत्रफल और आयतन]] | [[Category:पृष्ठीय क्षेत्रफल और आयतन]] | ||
[[Category:गणित]][[Category:कक्षा-10]] | [[Category:गणित]][[Category:कक्षा-10]] | ||
Revision as of 10:00, 29 August 2024
The volume of the combination of solids will be equal to the sum of the volume of individual solids.
Volume of a Combination of solids Formula
We get the volume of a combination of a solids by adding the volume of the individual solids. Hence, the formula to calculate the volume of a combination of solids is given by the formula,
Where
is the volume of the combination of solids
and are the volume of the individual solids such as solid , solid , and so on.
Volume of Solids Formula
Here are the formula for volumes of all the three-dimensional solid shapes.
For a cuboid which has length , breadth and height , the formula for volume and surface area is given by:
- Volume =
- Total surface area =
- Length of diagonal of cuboid =
For a cube having edge length equal to , the formula for volume and surface area is given by:
- Volume =
- Total surface area =
- Length of diagonal of cube =
Similarly, for other shapes
- Volume of Sphere =
- Volume of Cone =
- Volume of Cylinder =
- Volume of Hemisphere =
Example
A cylinder of volume cm3 is placed with a cone, whose height is cm. If the height of cone and cylinder is equal, then find the total volume of the shape formed by the combination of cylinder and cone.
Solution:
Given, Volume of cylinder cm3
Height of cylinder = Height of cone = cm
The formula for Volume of cylinder is
The formula for Volume of cone is given by:
By putting the value of from eq.
cm3
Therefore, the total volume of the combined solids, cm3
Note: Volume of Cone = (Volume of Cylinder)