Volume of Hemisphere

In this section we will discuss about Volume of Hemisphere.

Hemisphere : Half of a sphere cut by a plane passing through its center, we get hemisphere.
A hemisphere is half of a full sphere and the volume of a hemisphere is equal to two thirds multiplied by pi multiplied by radius to the power 3. So the formula to find the volume-hemisphere is :
Volume-Hemisphere = 2/3 π r3

Some solved examples :

1) How many liters of milk can a hemispherical bowl of diameter 10.5 cm hold?
Solution : Diameter = 10.5 cm
∴ radius = r = 5.25 cm
Volume = 2/3 π r
3
⇒ v = 2/3 x 3.14 x (5.25)
3
⇒ V = 302.91= 303 cm
3
∴ V = 0.303 liter
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2) A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m then find the volume of the iron used to make the tank.
Solution : As the iron sheet is 1cm = 0.01 m thick and the inner radius is 1m ( inner radius) so the radius of the tank becomes 0.01 + 1 = 1.01(outer radius) cm
Inner radius (r
1 ) of hemispherical tank = 1 m
Thickness of hemispherical tank = 1 cm = 0.01m
Outer radius (r
2 ) of hemispherical tank = (1+ 0.01) m = 1.01 cm
Volume of hemisphere = 2/3 π( r
23 - r 23 )
V = 2/3 x 3.14 x ( 1.01
3 - 1 3 ) 3
⇒ V = 2/3 x 3.14 (1.030301 – 1)
⇒ V = 2/3 x 3.14 x 0.030301
⇒ V = 0.06343 m
3
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3) A right circular cylinder having diameter 12 cm and height 15 cm is full with ice cream. The ice cream is to be filled in comes of height 12 cm and diameter 6 cm having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Solution : Diameter of cylinder = 12 cm ⇒ radius = r = 6 cm and height =h = 15 cm
∴ Volume of cylinder = π r
2 h
⇒ V = 3.14 x 6
2 x 15
⇒ V = 3.14 x 36 x 15 = 1695.6 cm
3
Diameter of cone = 6
∴ Radius of cone = radius of hemisphere = 3 cm
∴ volume of cone = 1/3 π r
2 h
V = 1/3 x 3.14 x 3 x 3 x 12 = 113.04 cm
3
And volume of hemisphere = 2/3 π r
3
V = 2/3 x 3.14 x 3 x 3 x 3 = 56.52 cm
3
∴ the total volume of cone = volume of cone + volume of hemisphere
⇒ V = 9.42 + 56.52 = 65.94
∴ Number of cones = ( Volume of cylinder ) / Total volume of cone
⇒ Number of cones = 1695.6 / 169.56
∴ Number of cones = 10

Volume :

Volume Formulas
Volume of Irregular Shape
Volume of Cube
Volume of Rectangular Prism(Cuboid)
Volume of Cylinder
Volume of Cone
Volume of Sphere
Volume of Hemisphere
Volume of Prism
Volume of Pyramid

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