In this section we will be learning problems involving conversions of solids from one shape to another with no change in volume.

**Conversion of Solids from one shape to another
with no change in Volume**

Conversions or Transformations becomes a common part of our daily
life. For example, a gold smith melts a bar of gold to transform it to a jewel.
Similarly, a kid playing with clay shapes it into different toys, a carpenter
uses the wooden logs to form different house hold articles/furniture. Likewise,
the conversion of solids from one shape to another is required for various
purposes.

In this section we will be learning problems involving conversions
of solids from one shape to another with no change in volume.

**Example 7.29 **A metallic sphere of radius** **16** **cm is melted and recast
into small spheres** **each of radius 2 cm. How many small spheres can be obtained?

** Solution **Let the number of small spheres obtained be

Let *r* be the radius of each small sphere and *R* be
the radius of metallic sphere.

Here, *R* = 16 cm, *r* = 2 cm

Now, *n*×(Volume of a small sphere) = Volume of big metallic
sphere

8*n* = 4096 gives *n *=* *512

Therefore, there will be 512 small spheres.

**Example 7.30**

A cone of height** **24** **cm is made up of modeling clay. A child reshapes
it in** **the form of a cylinder
of same radius as cone. Find the height of the cylinder.

** Solution **Let

Also, let *r* be the raius of the cone.

Given that, height of the cone *h*_{1} = 24 cm;
radius of the cone and cylinder *r* = 6 cm

Since, Volume of cylinder = Volume of cone

Therefore, height of cylinder is 8 cm

**Example 7.31 **A right circular cylindrical container of base
radius**
**6** **cm and height** **15** **cm is full of ice cream.
The ice cream is to be filled in cones of height 9 cm and base radius 3 cm,
having a hemispherical cap. Find the number of cones needed to empty the
container.

** Solution **Let

Given that, *h* = 15 cm, *r* = 6 cm

Volume of the container *V* = *πr*^{2}*h*
cubic units.

= (22/7) × 6 × 6 ×15

Let, *r*_{1} = 3 cm, *h*_{1} = 9 cm be
the radius and height of the cone.

Also, *r*_{1} = 3 cm is the radius of the
hemispherical cap.

Volume of one ice cream cone =(Volume of the cone + Volume of the
hemispherical cap)

Number of ice cream cones needed =

Thus 12 ice cream cones are required to empty the cylindrical container.

Tags : Solved Example Problems | Mensuration | Mathematics Solved Example Problems | Mensuration | Mathematics

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