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SURFACE AREAS AND VOLUMES | SPEED NOTES
Introduction :
We are familiar with the shapes of solids like right circular cylinder, right circular cone, sphere, cuboid, cube, box, brick, glass tumbler, ice-cream cone, etc. and we have also learnt how to find surface areas and volumes of these solids in our earlier classes.
In our day-to-day life, we must have seen many solids which are either a part or a combination of these solids, for example, a medicine capsule, oil tanker, funnel, conical flask, toys, test tubes, etc.
In this chapter, we shall learn to find surface areas and volumes or capacities of such solids.
Also, we shall deal with problems of conversion of solid from one form to another.
Cuboid:
(i) Volume of cuboid = lbh cubic units
(ii) Lateral surface area or Curved surface area of a cuboid =2(l+b)h sq. units
(iii) Total surface area of a cuboid =2(lb+bh+hl) sq. units
Cube :
Cube is a special case of cuboid in which length, breadth and height are equal (l = b = h).
(i) Volume of a cube =(edge)3 cubic units.
(ii) Lateral surface area or Curved surface area of a cube =4(edge)2 sq. units (iii) Total surface area of a cube = 6(edge)2 sq. units 2
(iv) Diagonal of a cube =√3 (edge) units.
Right Circular Cylinder :
(i) Volume of a right circular cylinder =πr 2 h cubic units (ii) Lateral surface area or Curved surface area of a right circular cylinder= 2πr sq. units
(iii) Total surface area of a right circular cylinder
= 2πr 2 + 2πrh =2πr(r+h) sq. units
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