Calculation formula of geometric surface area of space

The surface area of 1, regular prism and regular pyramid

Let the height of the prism be h and the perimeter of the polygon at the bottom be c, then the lateral area calculation formula of the straight prism is obtained:

S=ch, that is, the side area of a right-angled prism is equal to the product of its bottom perimeter and height.

The side development diagram of a regular pyramid is some congruent isosceles triangles with regular polygons at the bottom.

If the side length of the bottom surface is a, the perimeter of the bottom surface is c, and the inclined height is h', the lateral area formula of the regular N-pyramid is obtained.

S =1/2 * nah' =1/2 * ch', that is, the lateral area of a regular quadrangle is equal to half the product of the perimeter and the slope height of its bottom surface.

2. Surface area of prism

The side development of the prism is some congruent isosceles trapezoid,

Let the side length of the lower bottom surface of the prism be a, the perimeter of the prism be c, the side length of the upper bottom surface be a', the perimeter be c' and the inclined height be h', then the lateral area formula of the regular N prism can be obtained: s =1/2 * n (a+a') h' =1/2 (c+c').

3, the surface area of the ball

S=4πR？ That is to say, the spherical surface area is equal to four times the area of its great circle.

4. Surface area of frustum of a cone

The side development diagram of the frustum is a fan-shaped ring, and its surface area is equal to the area of the upper and lower bottom surfaces plus the area of the side surface, that is,

S=π(r '？ +r？ +r'l+rl)

Calculation formula of spatial geometric volume

1, cuboid volume

V=abc=Sh

2. Cylinder volume

All columns

V=Sh, that is, the volume of a cylinder is equal to the product of its bottom area s and its height h,

column

V=πr？ h、

Step 3: pyramids

V= 1/3*Sh

4. Cone

V= 1/3*πr？ h

5. Prism

V= 1/3*h(S+(√SS')+S ')

Step 6 truncate the cone

V= 1/3*πh(r？ +rr'+r '？ )

7. Ball

V=4/3*πR3