# Surface Areas and Volumes Class 10 Notes: Chapter 13

Surface Areas and Volumes Class 10 Notes provided here are one of the best resources that the students of class 10 can refer to and be thorough with all the concepts. The different topics from class 10 CBSE chapter 13 notes i.e. surface areas and volumes that are covered here are-

• What is surface area and volume
• Surface area and volume of some important figures
• Frustum of a right circular cone
• Example Question
• Practice Questions

## What is the Surface Area and Volume of a Figure?

Surface area is defined as the measurement of the surface of any solid figure. Surface area can be of two types-

1. Total surface area
2. Curved surface area or lateral surface area

Note: The Total Surface area includes the area of all the surfaces of the solid, whereas the curved surface area includes the area of the surfaces excluding the base and the top surface.

### Frustum of a Right Circular Cone

Frustum of a right circular cone is the resulting shape when a right circular cone is sliced by a plane parallel to its base and the smaller conical portion is removed. The total surface area, the curved surface area, and the volume of Frustum of a Right Circular Cone is given by-

 Curved surface area of a frustum of a cone $\pi\times l\left ( r_{1}+r_{2} \right )$ Total surface area of frustum of a cone $\pi\times l\left ( r_{1}+r_{2} \right ) + \pi\left ( r_{1}^{2}+r_{2}^{2} \right )$ Volume of a frustum of a cone $\frac{1}{3}\pi\times h\left ( r_{1}^{2}+r_{2}^{2}+r_{1}r_{2} \right )$

### Practice Questions

1. An iron rod has a diameter of 1 cm and a length of 8 cm. It is drawn into a wire of length 18 m of uniform thickness. Calculate the thickness of the wire.
2. Consider a cone having a height of 24 cm and radius of base 6 cm. If that cone is reshaped into a sphere, what would be the radius of that sphere?
3. 3 cubes having an equal volume of 64 cm3 are joined together end to end to form a cuboid. Calculate the surface area of the resulting cuboid.

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#### Practise This Question

The sides of ΔABC are 6cm, 8cm and 10cm. If the ratio of corresponding sides is 2, then find the sides of the larger triangle which is similar to ΔABC .