Question

all the formulas of mensuration​

Answer 1

Here is formula's of mensuration, provided by me.


Circumference & Area of a Circle
 Area of a Circle = π r2
.
 Perimeter of a Circle = 2 π r
 Area of sector = θ/360°(π r2
)
 Length of an arc = θ/360°(2π r).
 Area of ring = π.( R2
– r
2
)
 Distance moved by a wheel in one revolution = Circumference of the wheel.
 Number of revolutions = Total distance moved .
Circumference of the wheel.
Area of an equilateral triangle = \/3/4.(side)2
.
Note: While solving ‘Mensuration’ problems, take care of the following.
1. If diameter of a circle is given, then find the radius first
(Have you made mistake earlier by taking ‘d’ as ‘radius’ and solved the problem ?)
2. Check the units of the entire data. If the units are different, then convert them to the same units.
For Example: Diameter = 14 cm, and Height = 3 m
Therefore Diameter = 14 cm, and Height = 300 cm (Have you ever committed such mistake ?)


Solids
1. Cylinder: Volume of a cylinder = π r2
h
Curved surface area = 2 π r h
Total surface area = 2 π r h + 2π r2 = 2 π r ( h + r )
Volume of hollow cylinder = π R2
h – π r2
h = π ( R2
– r
2
) h
TSA of hollow cylinder = Outer CSA + Inner CSA + 2 . Area of ring.
2 π R h + 2 π r h + 2.
[π R2 – π r2
]
( Of course, If you want, you may take 2 π ‘common’ )
2. Cone: Volume of a Cone = ⅓ π r2
h.
CSA of a Cone = π r l ( Here ’l’ refers to ‘Slant height’) [ where l = √(h2 + r2
) ]
TSA of a Cone = π r l + π r2
= π r ( l + r )
3. Sphere: Surface area of a Sphere = 4π r2
. ( In case of Sphere, CSA = TSA i.e they are same)
Volume of hemi sphere = ⅔ π r3 [Take half the volume of a sphere]
CSA of hemisphere = 2 π r2 [Take half the SA of a sphere]
TSA of hemisphere = 2 π r2
+ π r2 = 3 π r2

Volume of spherical shell = Outer volume – Inner volume = 4/3.π.(R3 - r3
)
While solving the problems based on combination of solids it would be better if you take common.
 T.S.A. of combined solid = C.S.A of solid 1 + C.S.A of solid 2 + C.S.A of solid 3
 If a solid is melted and, recast into number of other small solids, then
Volume of the larger solid = No of small solids x Volume of the smaller solid
For Ex: A cylinder is melted and cast into smaller spheres. Find the number of spheres
Volume of Cylinder = No of sphere x Volume of sphere.
 If an ‘Ice cream cone with hemispherical top’ is given then you have to take
a) Total Volume = Volume of Cone + Volume of Hemisphere
b) Surface area = CSA of Cone + CSA of hemisphere (usually Surface area will not be asked)




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Thanking you

Shreyansh