## cube , cuboid , right circular cylinder and frustum/bucket | mensuration short tricks .

Today we are going to talk about some important arithmetic formulae on cube , cuboid , Right circular cylinder and frustum/bucket.

Students are advised to learn all the formulae on Keep practicing with it.
SOME IMPORTANT SUTRAS
* CUBE
1). Volume of cube = a^3 = d^3/3√3
2). Diagonal of the cube = a.√3
3). Surface area of cube = 6a^2
4). Side of cube = (V)^1/3 = d/√3
5). Surface area of cube = 2d^2
5). From the three small cube having volume V1 , V2  and V3 , a big cube are formed then side of the big cube = (V1+V2+V3)^1/3
6). Lateral surface area of cube = 4a^2
8). No of y sided cubes formed from the cube of  side x is = (x/y)^3
* CUBOID
1). Volume of cuboid = lbh
2). Length of cuboid = V/bh
3). Breadth of the cuboid = V/lh
4). Height of the cuboid = V/lb
5). Surface area of cuboid = 2(lb+bh+hl)
6). Lateral surface area of cuboid = 2(l+b)h
7). If surface area of cuboid is x , y and z respectively , then xyz = V^2
8). Diagonal of cuboid = √(l^2+b^2+h^2)
* RIGHT CIRCULAR CYLINDER
1). Curved surface area of cylinder = 2πrh
2). Total surface area of cylinder = 2πr(r+h)
3). Volume of cylinder = πr^2h
4). Volume of hollow cylinder = πh(R^2-r^2)
5). Total surface area of hollow cylinder =
2π(R+r)(R-r+h)
6). Width of hollow cylinder = R-r
7). No of cylinder of r1 radius and h1 height , which is formed from the cylinder of radius r and height h is = r^2.h/r1^2.h1
8). Total Curved surface (inner and outer) area of hollow cylinder =
2πh(r1+r2)
9). Volume of capsule = πr^2[(4r/3)+h]
* BUCKET/FRUSTUM
1). Slant height of the frustum = √[h^2+(R-r)^2]
2). Curved surface area of frustum = πl(R+r)
3). Total surface area of frustum =
πl(R+r)+πr^2
4). Volume of frustum = πh(R^2+r^2+Rr)/3
5). Total surface area of solid frustum =
πl(R+r)+π(R^2+r^2)
* RIGHT CIRCULAR CONE
1). Curved surface area of cone = πrl
2). Total surface area of cone = πr(l+r)
3). Volume of cone = πr^2.h/3
4). Slant height of cone = √(r^2+h^2)
5). Height of cone =  √(l^2-r^2)
6). Radius of cone =  √(l^2-h^2)
7). Volume of the cone = 1/3 times the volume of cylinder.
8). If radius of cone become m times then the volume become = m^2 times
9). If radius of cone become n times then it’s volume become n times.

#### Suchit prajapati

A person who always imagines, learner and knowledge enthusiast. My imagination is my power.