July 9, 2018

# Formula for the cone surface and volume

Formula for the cone surface: SA = B + LA, where SA refers to the surface, B refers to the surface of the base, and LA refers to the lateral area.

This formula is exactly the same as the initial formula for the pyramid. CAUTION! This formula will be very different and can be difficult to remember. In other situations, I only advised to remember this initial formula and then replace the corresponding pre-learned polygon formula. This time, however, things are different. The shape we get when we open the cone is NOT any of the polygons we learned earlier and we will need some new terminology.

For the cone, the base is a circle so that the first change in the initial formula looks like SA = pi r ^ 2 + LA. This is a side area that will bring us trouble.

The image that creates a vertical line in the shell like Indian dark tea and then opens it and places the open shape straight. The shape will look like a big pizza, but that will not be the whole pizza. Now, using the same “limiting” method we used to calculate the circle area, we will mentally embed it in many parts and put them together by moving the point and lowering. Again, we will use “taking the boundaries” of this procedure. The end result of this process is a rectangle whose length is half the circumference of the basic circle – 1/2 (2 pi r) or pi r whose height is the hair height s.

End height is a new terminology we must learn. While the height of the cone is vertical to the ground, high hair is the height of the side of KONE. This is the height of the material (skin) from the roasting of the ground measured from top to bottom. This is the length or height of the side edges of the side.

The final replacement SA = B + LA becomes SA = (pi r ^ 2) + (pi r) s, where the radius of the lower circle and the hair is the height of the side of the cone.

Uh! Now you understand why I said you should remember this final formula. Fortunately, the volume formula is not so complicated.

Formula for the Volume of a cone: V = (1/3) B h, where B AREA is base and h is the height of conical perpendicular. 1/3 comes from the fact that, as in the case of pyramids and prisms, 3 cylinder filling nozzles should be fitted with the same base and height. Thus, V = (1/3) B h becomes V = (1/3) (pi r ^ 2) h.

**Summarize:**

(1) The cone surface formula is SA = B + SA or SA = pi r2 + pi r s; and the area is always measured in square units.

(2) The cone volume formula is V = (1/3) B h or V = (1/3) pi r2 2 h; and volume is always measured by cubic units.