# Volume of Cone

Volume of Cone : From the above diagram we can see that there is right circular cylinder and a right circular cone of the same base radius and same height.

When fill up cone up to the brim is emptied into the cylinder 3 times then the cylinder will be completely filled up to the brim. So from that we can conclude that cone volume is 1/3 rd that of the volume of the cylinder.

The formula is :

volume of - cone = 1/3 π r
^{2} hl ^{2} = r^{2} + h^{2} |

**Some solved examples :**

1) Find the volume of a cone the radius of whose base is 21 cm and height is 28 cm.

**Solution :**r = 21 cm and h = 28 cm

Volume of cone = 1/3 π r

^{2}h

V = 1/3 ( 3.14 x 21 x 21 x 28)

V = 1/3 x 38772.72

∴ Volume of a cone = 12924.24 cm

^{3}

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2) If the height of a cone is 15 cm and its volume is 770 cu.cm; find the radius of its base.

**Solution :**h = 15 cm and V = 770 cu.cm

volume of cone = 1/3 π r

^{2}h

⇒ 770 = 1/3 x 3.14 x r

^{2}x 15

⇒ 770 = 3.14 x r

^{2}x 5

⇒ 770 = 15.7 x r

^{2}

⇒ r

^{2}= 770 / 15.7 = 49

⇒

^{2}= 49

∴ r = 7 cm.

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3) A right triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so obtained.

**Solution :**As the triangle revolved about the side 12 cm.

∴ radius = r = 5m and height = h = 12 cm

Volume = 1/ 3 π r

^{2}h

V = 1/3 x 3.14 x 5 x 5 x 12

V = 314 cm

^{3}

**Volume :**

• Volume Formulas

• Volume of Irregular Shape

• Volume of a Cube

• Volume of a Rectangular Prism(Cuboid)

• Volume of a Cylinder

• Volume of Cone

• Volume of a Sphere

• Volume of a Hemisphere

• Volume of a Prism

• Volume of a Pyramid

• Volume Formulas

• Volume of Irregular Shape

• Volume of a Cube

• Volume of a Rectangular Prism(Cuboid)

• Volume of a Cylinder

• Volume of Cone

• Volume of a Sphere

• Volume of a Hemisphere

• Volume of a Prism

• Volume of a Pyramid

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