A conical tent is to accommodate 77 persons. Each person must have 16m³ of air to breathe. Given the radius of the tent as 7m find the height of the tent and also its curved surface area.

Answer:

Total air in the tent =77×16=1232 m 3 (which is the total volume of tent) Since the tent is conical we will use some formula of cone: Volume= 31πr 2h ; Curved surface area=πrl l= slant height & r=7m Volume = 31πr 2h= 31π(7 2)h= 31 7227 2h= 3154h And we eknow that total volume is 1232m 3 So, 1232= 3154h h= 1541232×3=24m

Step-by-step explanation:

Final answer:

To solve this problem, we need to use the volume formula of a cone and equate it to the total volume of air needed by the 77 persons. Once we solve for the height, we can then determine the curved surface area of the cone using the radius and height.

Explanation:

This mathematics problem can be solved using the formula for the volume of a cone, which is given by V = 1/3 * π * r² * h where “r” stands for the radius of the base of the cone, “h” corresponds to the height, and “π” is a constant that roughly equals to 3.14. To accommodate 77 persons, with each person needing 16 m³ of air to breathe, the total volume necessary would be 77 * 16 = 1232 m³. Setting this equal to the volume of the cone formula and plugging in the given radius (r = 7 m), we solve for the height. Simultaneously, the curved surface area of a cone is given by A = π * r * l = π * r * sqrt((r²)+(h²)). We can evaluate both the height of the tent and its curved surface area applying these equations.

Learn more about Volume and Surface Area of Cone here:

brainly.com/question/33666909

#SPJ11