# Important Geometry Formulas-Volume & Surface area

### 1. CUBE

• Volume =
• Surface area of cube =
• Diagonal of the cube =

### 2. CUBOID

• Volume = lbh
• Surface area = 2(lb + bh +lh)
• Diagonal of cuboid =

### 3. Room

(Rectangular room has 4 walls and opposite walls have equal areas)

• Total area of walls =
• Total volume of the room = lbh
• Area of floor or roof =

### 4. BOX

• Surface area of an open box =  =
• Capacity of box =
• Volume of the material of the box = External volume –Internal volume(or capacity)

### 5. CYLINDER

• Volume = Area of base × height =
• Curved Surface Area =Perimeter of base × height=
• Total Surface Area =C.S.A + 2 × Area of one circular end=

### 6. HOLLOW CYLINDER

• Volume =
• Curved Surface Area =
• Total Surface Area of Hollow Cylinder =

### 7. CONE

• Volume =
• Slant Height (l) =
• Curved Surface Area =
• Total Surface Area=
• If cone is formed by sector of a circle then.
(a) Slant height = radius of circle
(b) circumference of base of cone = length of arc of sector
• Radius of maximum size sphere in a cone =

where , r is radius of cone; l is slant height of cone and h is height of cone.

• If cone is cut parallel to its base and ratio of heights, radius or slant height of both parts is given as x : y. Then ratio of there volume =

### 8. FRUSTUM OF CONE

• Slant Height (l)=
• Curved Surface Area =
• Total Surface Area =
• Volume =

### 9. SPHERE

• Volume =
• Total Surface Area =
• If a sphere is cut into n parts, then T.S.A of n parts =  +

### 10.  HOLLOW SPHERE OR SPHERICAL

• Volume =
• Internal Surface Area =
• External Surface Area =

### 11. HEMISPHERE

• Volume =
• Total Surface Area=
• Curved Surface Area=

### 12. RIGHT PRISM

• Volume = Area of Base  Height
• Lateral Surface Area = Perimeter of base   Height
• Total Surface Area = Lateral  Surface Area + 2   Area of Base

### 13. PYRAMID

For Triangular Pyramid

• Volume =  Area of Base  Height
• Total Surface Area = Area of Base   Area of Slant Surface
• Base =abc
• Slant Surface =abd+bcd+acd

### For Square Pyramid

• Volume =   Area of abcd  Height
• Total Surface Area = Area of abcd + Area of (apd+dpc+pcb+apb)
• Base =abcd
• Slant Surface =apd+dpc+pcb+apb

### 14. TETRAHEDRON

Height =

Volume =

Lateral Surface Area=

Total Surface Area =

Slant Height =

Slant Edge = a

### IMPORTANT POINTS TO REMEMBER

1. If length, breadth and height of a cuboid are increased by x%, Y% and z% then its volume increased by

2. If side of a cube is increased by x% then its volume increases by

3. If the radius (or diameter) of a sphere is changed by x% then its volume changed by

4. If height of a cylinder is changed by  and radius remains the same then the volume changes by .

5. If radius of a cylinder is changed by   and height remains unchanged , then volume changes by

6. If radius of a cylinder or cone is changed by x% and height is changed by y% , then volume changes by

7.  If in a cylinder or cone , height & radius both change by x% , then volume changes by

8. If radius a share or edge of a cube is changed by x%, then the change in surface area is given by

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