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.