Frustum of a Cone-Total Surface Area

This frustum has volume and surface area such as other 3D shapes. There are a lot of formulas that have been described in the discussion chapter. Any shape’s net has been combined with the shapes of two dimensions that have been gained from 3D shapes. The frustum of correspondence gets structured when the frustum net is folded up. The frustum cone possesses two circles accompanying its bases of two circles.  

Frustum of a cone

Cut the circular cone on its right side In parallel with the plane to the cone’s base, after cutting according to this position, the shape of the solid between the cone’s base and the plane is described as the frustum cone. For example, the ports of flowers have the frustum cone shape. The volume and surface area of this cone may be determined and calculated using some standard formulas. The frustum cone’s CSA = (r1 + r2) pi*l. In this formula, r1 is the radius of the major circular face, slant height has been presented as l,  r2 has been represented as the radius of the mini circular face. The formula of slant height is l = √(r1 –  r2) + h², here h has been represented as the frustum’s height. The formula of frustum cone’s TSA = pi*r1² + pi*r2² + pi*l(r1+ r2), and the formula of frustum cone’s volume = (⅓)pi*h(r1r2 + r1² +r2² ). The Latin word frustum means a “piece cut off”. While a solid is cut in such a portion that the plane cutting and the solid base are placed that they become parallel to each other. In this position, they make a frustum. The other part of the solid is placed between its base and plane of parallel cutting.  

Frustum of a Cone Total Surface Area

The frustum is a solid’s portion in the geometry that reclines between two planes parallelly by cutting it. By cutting the plane’s right circular cone to its base, the solid portion between its base and plane has been known as the cone’s frustum. Plane after cutting the circular cone’s right portion, the base will become a frustum. The frustum cone’s volume = “1/3× pi  × h(R² + r² + R*r)”, here r = smaller circle’s radius, R = bigger circle’s radius, h = the frustum’s height. The formula of CSA = “ pi * l(r+R)”, where r = the radius of the small circle, R = the radius of the big circle, l = the frustum’s slant height. The CSA is the abbreviated form of “curved surface area”. For example, to understand a frustum properly, you have to memorize the ice cream that is filled with ice and creams. When the top of this ice cream gets cut, the frustum cone takes place. The remaining part of this ice cream converts into a cone of a frustum. By using formulas, the volume of frustum may be calculated easily with examples. Assume a top cutting cone as the frustum cone which has the height h units, slant l units, radius r units. In this cone, the left side corner is named cone 1 and the right one is named cone 2. The total height of this frustum is assumed H and slant height L. Then the right cone’s volume will be = pi*r²h * ⅓, similarly, the volume of cone 2 will be the same.  

Frustum of a cone total surface area formula

The formula of TSA = “ pi× l ( r+R) + (r ²+R²) pi, here, l = the frustum’s slant height, r = the radius of the smaller circle, R = the radius of the bigger circle. Here to understand the formula clearly and easily, an example has been provided. Suppose, the smaller circle’s radius is 3, the frustum’s height is 12, the bigger circle’s radius is 8, and the frustum’s slant height is 13, then the output will be in such a form like a frustum’s cone volume = 1218.937, the frustum cone’s surface area totally will be 678.58344, and the frustum cone’s CSA = 449.24738. Another example of this formula has been taken to understand the concept of the frustum cone. If the mini circle radius is 7, height is 4, slant height is 5, and the major circle radius is 10, then the output will be produced in such a way like the cone volume of frustum = 917. 34436, frustum cone of TSA = 735.1321, frustum cone CSA = 267.03516.

Conclusion

In conclusion, it may be explained that the frustum cone is described as pyramids and cones. Besides this definition, it is also characterized by the term truncated shape. This frustum may differ according to a specific shape and their structure also are different from each other. Some of them are the cone’s frustum, triangular pyramid, square pyramid’s frustum. All of them possess different definitions, surfaces, and volumes according to their structure. The frustum cone’s net is the combination of two shapes in different dimensions.