### 1. AREA AND VOLUME OF A PRISM

The area of a prism is equal to the sum of the areas of its bases* B and the area of its shell ** M*, ie.

**P = 2B + M**

The volume of a prism is equal to the product of the area of the base B * a*nd the height of the pris

*H, ie.*

**m****V = B • H**

### 2 AREA AND VOLUME OF THE PYRAMID

The area of the pyramid is equal to the sum of the area of the base B * a*nd the mantle

*M, ie.*

**R = B + M**

The volume of any pyramid is equal to one third of the product of the area of the base and the length of its height, ie

### 3. AREA AND VOLUME OF A CUTTING PYRAMID

The area of a truncated pyramid is equal to the sum of the areas of its bases B and* *B₁

*d the sheath*

**an***M, ie.*

*Р = В + В₁ + M*

If the height of the truncated pyramid * i*s H, and the areas of the base

*ar*

**s***B and B₁, then its volume is*

**e**### 4. AREA AND CYLINDER VOLUME

The area of a cylinder is equal to the sum of the areas of the base B* *and the casing

*M, ie.*

** P = 2B +** M, ie P

*= 2πR (R + H)*The volume of any cylinder is equal to the product of the area of its base and height, ie.

### 5. AREA AND VOLUME OF CONE

The area of a cone is equal to the sum of the area of the base B * a*nd the sheath

*M, ie.*

*+ M, ie*

**R = B***,*

**R = πR (R + s)*** (*R – radius of the base,

**ѕ – generatrix).**

The volume of any cone is equal to one third of the product of the area of

the base and its height, ie.

### 6. AREA AND VOLUME OF CUTTED CONE

The area of a truncated cone is equal to the sum of the areas of the two bases and the area of its casing, ie.

**P = π [ R² + r² + s (R + r)]**

The volume of a truncated cone is calculated by the formula:

### 7. BALL VOLUME AND BALL PARTS

The volume* *V of a ball of radius

*is calculated by the formula*

**R**The volume* *V of a ball slice is calculated by the formula

in which * R* is the radius of the ball,

*h is the height of the dome.*

The volume* *V of a ball segment with height

*and radius of the bal*

**h***R is calculated by the formula*

**l**

The volume* V* of a ball layer with height

*h and radii of the boundary circles*

*and*

**r1***2 (Fig.23) is calculated by the formula*

**r**