Let r and h be the radius and height of a cone then its volume

**Volume of a right circular cone**

Let *r* and *h* be the radius and height of a cone then
its volume

V = 1/3 × *πr*^{2}*h* cu. units.

**Demonstration**

·
Consider a right circular cylinder and three right circular cones
of same base radius and height as that of the cylinder.

·
The contents of three cones will exactly occupy the cylinder.

From, Fig.7.28 we see that,

3× (Volume of a cone) = Volume of cylinder

*= πr *^{2}*h *cu. Units

Volume of a cone = 1/3 *πr*^{2}*h* cu. Units

The volume of a solid right circular cone is** **11088** **cm^{3}. If its
height is**
**24** **cm** **then find the radius of
the cone.

Let* **r*** **and

Given that, volume of the cone = 11088 cm^{3}

Therefore, radius of the cone *r*=21 cm

**Example 7.20 **The ratio of the volumes of two cones is** **2:3. Find the ratio of
their radii if** **the height of second cone is double the height of the first.

** Solution **Let

Therefore,
ratio of their radii = 2 : √3

Tags : Definition, Formula, Solved Example Problems | Mensuration | Mathematics , 10th Mathematics : Mensuration

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10th Mathematics : Mensuration : Volume of a right circular cone | Definition, Formula, Solved Example Problems | Mensuration | Mathematics

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