लम्ब वृत्तीय शंकु का आयतन: Difference between revisions
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A cone can be seen as a set of non-congruent circular disks that are stacked on one another such that the ratio of the radius of adjacent disks remains constant. | A cone can be seen as a set of non-congruent circular disks that are stacked on one another such that the ratio of the radius of adjacent disks remains constant. | ||
शंकु का आयतन = <math>\frac{1}{3}\pi r^2 h</math> | |||
where <math>r</math> is the base radius and <math>h</math> is the height of the cone. | where <math>r</math> is the base radius and <math>h</math> is the height of the cone. | ||
== | == उदाहरण == | ||
1. | 1.एक शंकु की ऊंचाई और तिर्यक ऊंचाई क्रमशः <math>21</math> cm और <math>28</math> cm है। | ||
शंकु का आयतन ज्ञात कीजिए। | |||
हल: | |||
<math>l^2=r^2+h^2</math> से | |||
<math>r=\sqrt{l^2 -h^2}</math> | <math>r=\sqrt{l^2 -h^2}</math> | ||
| Line 21: | Line 21: | ||
<math>r=\sqrt{28^2 -21^2}=\sqrt{784 -441}=\sqrt{343}=\sqrt{49 \times 7}=7\sqrt{7}</math> cm | <math>r=\sqrt{28^2 -21^2}=\sqrt{784 -441}=\sqrt{343}=\sqrt{49 \times 7}=7\sqrt{7}</math> cm | ||
शंकु का आयतन = <math>\frac{1}{3}\pi r^2 h</math> | |||
=<math>\frac{1}{3}\times \frac{22}{7}\times (7\sqrt{7})^2 \times 21=7546</math> cm<sup>3</sup> | =<math>\frac{1}{3}\times \frac{22}{7}\times (7\sqrt{7})^2 \times 21=7546</math> cm<sup>3</sup> | ||
[[Category:पृष्ठीय क्षेत्रफल और आयतन]][[Category:कक्षा-9]][[Category:गणित]] | [[Category:पृष्ठीय क्षेत्रफल और आयतन]][[Category:कक्षा-9]][[Category:गणित]] | ||
Revision as of 09:52, 10 September 2024
The volume of a cone defines the space or the capacity of the cone. A cone is a three-dimensional geometric shape having a circular base that tapers from a flat base to a point called apex or vertex. A cone is formed by a set of line segments, half-lines or lines connecting a common point, the apex, to all the points on a base that is in a plane that does not contain the apex.
A cone can be seen as a set of non-congruent circular disks that are stacked on one another such that the ratio of the radius of adjacent disks remains constant.
शंकु का आयतन =
where is the base radius and is the height of the cone.
उदाहरण
1.एक शंकु की ऊंचाई और तिर्यक ऊंचाई क्रमशः cm और cm है।
शंकु का आयतन ज्ञात कीजिए।
हल:
से
cm
शंकु का आयतन =
= cm3
