Volume of solids, cuboid, cube, cylinder, cone, sphere, frustum of a cone,

VOLUME OF SOLIDS

CUBOID - It has 6 panels and each panel is rectangular. 

let length = l cm, width = b cm, height = h cm,

(i) Cuboid volume = ( l ✕ b  ✕ h ) Cubic Centimeter 

(ii) Diagonal of cuboid =   cm

(iii) Area of the entire surface of the cuboid = 2 (lb + bh +lh) square centimeter 

CUBE - It has 6 panels and each panel is square. 

let side of the cube = a cm

(i) Cube volume = a ✕ a ✕ a  Cubic Centimeter 

(ii) Diagonal of cuboid =  √3a  cm

(iii) Area of the entire surface of the cuboid = 6 (a✕a)  square centimeter

CYLINDER - Let the radius of the base of the cylinder = r cm

and height of the cylinder = h cm

(i) Volume of the cylinder = ( π r✕r h) Cubic Centimeter

(ii) Area of curved surface of cylinder = 2πrh square centimeter 

(iii) Area of the entire surface of the cylinder = ( 2πrh + 2πr✕r ) square centimeter

CONE - Let the radius of the base of the cone = r cm, height = h cm, and Oblique height = l cm

(i) l = 

(ii) Volume of cone = Cubic Centimeter

(iii) Area of curved surface of cone = πrl square centimeter 

(iv) Area of the entire surface of the cone = ( πrl + πr✕r ) square centimeter

SPHERE - Let radius of the sphere = r cm

(i) Volume of sphere = Cubic Centimeter

(ii) Area of curved surface of sphere = (4πr✕r) square centimeter

(iii)  Volume of half-sphere = Cubic Centimeter

(iv) Area of curved surface of half-sphere = (3πr✕r) square centimeter

FRUSTUM OF A CONE - Let the radius of base and vertex of Frustum of a cone R cm and r cm respectively. and height = h cm and Oblique height = l cm

(ii) Volume of Frustum of a cone = Cubic Centimeter

(iii) Area of Oblique of Frustum of a cone = πl(R+r) square centimeter, where

(iv) Area of the entire surface of the cone = ( base area ) + ( area of vertex ) + ( Curve surface area) centimeter square
={πR✕R+πr✕r+πl(R+r)} centimeter square

= π{ R✕R + r✕r + l(R+r)} centimeter square


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