- Books Name
- Rakhiedu Mathematics Book

- Publication
- Param Publication

- Course
- CBSE Class 10

- Subject
- Mathmatics

**Surface area and volume of combination of solids **

In this section we shall find the surface area and volume of solids which are combination of two or more solids.

Consider a circus tent shown in the given figure.

It consists of two parts I and II. Part-I is in the shape of a cone and Part-II is in the form of a cylinder.

Total surface area of the circus tent = Curved surface area of part-I i.e., cone + Curved Surface area of part-II i.e., Cylinder.

**Illustration 6**

A solid is composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and the radius of each hemispherical end is 7 cm, find the

**Solution : **

The whole length of the solid = 104 cm

The radius of each hemisphere = 7 cm

Therefore, the length of the cylindrical part of the solid = (104 – 2 x 7) cm = 90 cm Now, the total surface area of the solid

= 2 x (curved surface area of hemisphere) + (curved surface area of cylindrical part)

**Volume of Combination of Solids :**

In the previous section, we have studied about the surface area of solids made of two or more solids. There we find that while calculating the surface area of a solid, some surface areas are not included. But, here we will find the total volume of a solid which is also the actual volume of two or more combined solid.

**Illustration 7**

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toy. (Take p = 3.14)

**Solution : **

Let BPC be the hemisphere and ABC be the cone standing on the base of the hemisphere

**Conversion of Solid from One Shape to Another**

Some solids like candle, clay etc. can be changed into any shape. But the volume of the both solid shapes are same. For example, if a candle which is generally in the shape of a cylinder can be changed into any shape, but the volume remains same.

If a solid is transformed into a number of small identical solids of same or a different shape, then