The word 'circus' has the same root as 'circle'. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd. A circus tent is cylindrical upto a height of 8 m and conical above it. The diameter of the base is 28 m and total height of tent is 18.5 m . (i) Find slant height of the conical part. 1 (ii) Determine the floor area of the tent. 1 (iii) (a) Find area of the cloth used for making tent. 2 2
Explanation
This question asks us to find the total volume of air inside an empty tent. We can use the formula for the volume of a cylinder and a cone to find the total volume: V = πr^2h + (1/3)πr^2h', where r is the radius of the base, h is the height of the cylinder, and h' is the height of the cone. We are given the diameter of the base (28 m), the height of the cylinder (8 m), and the total height of the tent (18.5 m). We can find the height of the cone by subtracting the height of the cylinder from the total height: h' = 18.5 - 8 = 10.5 m. Now we can find the volume of the cylinder and the cone, and add them together to find the total volume: V = π(14)^2(8) + (1/3)π(14)^2(10.5) = 1551.5 m^3.
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