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 and the height of the prism H, ie.
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 and 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 and the sheath M, ie.
Р = В + В₁ + M
If the height of the truncated pyramid is H, and the areas of the bases are B and B₁, then its volume is
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 and the sheath M, ie.
R = B + M, ie
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 R is calculated by the formula
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 h and radius of the ball R is calculated by the formula
The volume V of a ball layer with height h and radii of the boundary circles r1 and r2 (Fig.23) is calculated by the formula
