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 r2 h
l2 = r2 + h2

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

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