1. Volume of sphere
2. Volume of a hollow sphere / spherical shell (volume of the material used)
3. Volume of solid hemisphere
4. Volume of hollow hemisphere (volume of the material used)

Let *r* be the radius of a sphere then its volume is given by
*V* = 4/3 *πr*^{3} cu.
units.

**Demonstration**

·
Consider a sphere and two right circular cones of same base radius
and height such that twice the radius of the sphere is equal to the height of
the cones.

·
Then we can observe that the contents of two cones will exactly
occupy the sphere.

From the Fig.7.30, we see that

Volume of a sphere = 2 × (Volume of a cone)

where the diameters of sphere and cone are equal to the height of
the cone.

Volume of a sphere = 4/3 *πr*^{3} cu. Units

Let *r* and *R* be the inner and outer radius of the
hollow sphere. Volume enclosed between the outer and inner spheres

Volume of a hollow sphere = 4/3 *π(R*^{3} − *r*^{3}
) cu. Units

Let *r* be the radius of the solid hemisphere.

Volume of the solid hemisphere = ½ (volume of sphere)

Volume of a solid hemisphere = 2/3 *πr*^{3 }cu.
Units

Let *r* and *R* be the inner and outer radius of the
hollow hemisphere.

Volume of a hollow hemisphere = 2/3 *π(R*^{3} − *r*^{3}
) cu. Units

**Example 7.21 **The volume of a solid hemisphere is** **29106** **cm^{3}. Another
hemisphere whose** **volume is two-third of the above is carved out. Find the radius of
the new hemisphere.

** Solution **Let

Given that, volume of the hemisphere = 29106 cm^{3}

Now, volume of new hemisphere = 2/3 (Volume of original sphere)

= 2/3 × 29106

Volume of new hemisphere = 19404 cm^{3}

2/3* πr *^{3}* *= 19404

Therefore, *r *=* *21* *cm

**Example 7.22 **Calculate the weight of a hollow brass sphere if
the inner diameter is** **14** **cm** **and thickness is 1mm, and whose density is 17.3 g/ cm^{3}.

** Solution **Let

Given that, inner diameter *d* = 14 cm; inner radius *r*
= 7 cm; thickness = 1 mm = 1/10 cm

Outer radius *R* = 7 + 1/10 = 71/10 = 7.1 cm

But, weight of brass in 1 cm^{3} = 17.3 gm

Total weight = 17.3×62.48 = 1080.90 gm

Therefore, total weight is 1080.90 grams.

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

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