# 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