Surface Area and Volumes Class 10 Notes Maths Chapter 13

CHAPTER AT A GLANCE

1. Right Circular Cylinder:

A right circular cylinder is solid generated by the revolution of a rectangle about of its sides.
NOTE : If a paper cylinder open at both the ends is cut along a vertical line on the curved surface and stretched on a plane surface, we obtain a rectangle of length i.e., 2rcr and breadth= Height of cylinder h.
So, curved surface area (C.S.A) or lateral surface area= 2pir x height
Important Formula for Cylinder

(I) C.S.A of cylinder

2. Hollow Cylinder’s Formulae e.g., (Rubber tubes pipes, etc.)
(i) Volume of material = Exterior volume- Interior volume

NOTE : (i) Two end faces of right circular cylinder are circles having each area= rcr2
(ii) Mass of cylinder= Volume x density
(iii) When rectangular sheet of paper is rolled along its length , we get a cylinder whose base circumference is length of sheet and height is same as breadth of sheet.

3. Cone
From figure, AO= height of cone and is denoted by’h’

Important Formula of rt. Circular Cone:

4. Frustum of a Cone

Frustum: A cone is cut by a plane parallel to the base of the cone,

5. Important Formula for Sphere and Hemi-sphere

6. Important Formula for Spherical Shell/ Hemispherical Shell

7. Surface Areas of a Combination of Solids

8. Volume of a Combination of Solids
Whenever solid is formed by combining two or more solids, then the amount of matter present in the new solid is equal to the sum of amounts of matter in the constituting solids. Volume of new solid = sum of the volumes of the individual solids

9. Conversion of Solid form One Shape to Another
(I) When a solid is converted from one shape to other, then its volume remains same only its shape and size changes.
(ii) a solid is converted into a number of small identical solids, then Number of small items
= Volume of larger object/ Volume of smaller object

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