Page 1 Surface Areas and Volumes Page 2 Surface Areas and Volumes Total Surface Area (2D) Shape Lateral/ Curved Surface Area p r r ( + l ) 2lb + 2bh + 2lh 2(l + b) x h 4 p r 2 3 p r 2 2 p r 2 4 pr 2 2 pr 2 p r h 2 p r h 2 3 1 _ 4 p r 3 _ 3 2 p r 3 _ 3 6 2 l 4 2 l Volume (3D) lbh Cube Sphere Diagonal of Cuboid ; Slant height of Cone (l ) ; Slant height of Frustum (l ) Surface Area: It is the sum of the total exposed area of a three dimensional solid object. It’s unit can be cm 2 , m 2 etc. Volume: It is the amount of space occupied by an object. It’s unit can be cm 3 , m 3 , etc. Cuboid Cylinder Frustum Hemisphere Cone pr r h ( ) 2 + prh 2 prl pl (R + r) p r r r r 3 1 _ ( ) 2 1 1 2 2 2 h + + 1 2 p p r r r r ( ) ( ) l 2 1 2 2 + + + l 3 r h l b h l l l r h r1 r2 h l r o r o (Solid) (Hollow) = l 2 + b 2 + h 2 = h 2 + r 2 = h 2 + (r 1 - r 2 ) 2 Surface Areas & Volumes SURFACE AREAS & VOLUMES 30 Page 3 Surface Areas and Volumes Total Surface Area (2D) Shape Lateral/ Curved Surface Area p r r ( + l ) 2lb + 2bh + 2lh 2(l + b) x h 4 p r 2 3 p r 2 2 p r 2 4 pr 2 2 pr 2 p r h 2 p r h 2 3 1 _ 4 p r 3 _ 3 2 p r 3 _ 3 6 2 l 4 2 l Volume (3D) lbh Cube Sphere Diagonal of Cuboid ; Slant height of Cone (l ) ; Slant height of Frustum (l ) Surface Area: It is the sum of the total exposed area of a three dimensional solid object. It’s unit can be cm 2 , m 2 etc. Volume: It is the amount of space occupied by an object. It’s unit can be cm 3 , m 3 , etc. Cuboid Cylinder Frustum Hemisphere Cone pr r h ( ) 2 + prh 2 prl pl (R + r) p r r r r 3 1 _ ( ) 2 1 1 2 2 2 h + + 1 2 p p r r r r ( ) ( ) l 2 1 2 2 + + + l 3 r h l b h l l l r h r1 r2 h l r o r o (Solid) (Hollow) = l 2 + b 2 + h 2 = h 2 + r 2 = h 2 + (r 1 - r 2 ) 2 Surface Areas & Volumes SURFACE AREAS & VOLUMES 30 Shape Formula Combination of Solids Area Volume Area Volume Area Volume 4p r + 2pr h 2 p rl + 2 p r 2 6l 2 - 2pr 2 l 3 - p r 2 l 4 p r 3 + p r 2 h 3 _ 2 p r 3 + p r 2 h 3 _ 1 3 _ Area Volume 2p r + 2prh + pr l 2 1 2 p r 3 + p r 2 h + p r 2 h 3 _ 1 3 _ 2 1 PLEASE KEEP IN MIND SURFACE AREAS & VOLUMES 31 Surface Area of Sphere Surface Area of Cube, Cuboid and Cylinder Volume of Cube, Cuboid and Cylinder Amazing Tricks to Understand Mensuration (surface areas and volumes) Formulae Scan the QR Codes to watch our free videos But for surface area until and unless it is said that both the surface areas are equal, one cannot equate it with the formula. ? When a form of solid is converted into another one, surface area may change but volume remains the same. Hence, we equate the formula of volume of the other object, to the value (in numbers) of the volume of the original object to know the value of the new parameter. ? ? For Volume of the combination of solid objects, simply take the sum of the volume of all the objects involved. ? Please make a note: Units for volume is written as (unit) 3 and that of surface areas is (unit) 2 . ? For surface area of combination of the solid objects, only look at the uppermost/the exposed portion of the objects. ................. .................. ............ < h > . r .............................................. ................. ........................ .............. l < > . r h ............. .............. ........... ........ ........... ............... ........... < > < > < > . r l l l ........... ............. ........... ............ ................ ........... < > . r h 1 < > l h 2Read More

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

1 videos|13 docs