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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.
Based on the above, answer the following questions :
(i) Find slant height of the conical part.
(ii) Determine the floor area of the tent.
(iii) (a) Find area of the cloth used for making tent.
OR
(iii) (b) Find total volume of air inside an empty tent.
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.
Based on the above, answer the following questions :
(i) Find slant height of the conical part.
(ii) Determine the floor area of the tent.
(iii) (a) Find area of the cloth used for making tent.
OR
(iii) (b) Find total volume of air inside an empty tent.
Show SolutionHide Solution↓
(i) Height of conical part $= 18.5 - 8 = 10.5$ m
Radius of conical part $= 14$ m
Slant height $= \sqrt{(10.5)^2 + (14)^2} = 17.5$ m
(ii) Floor area $= \frac{22}{7} \times 14 \times 14 = 616$ m$^2$
(iii) (a) Area of cloth used
$= 2 \times \frac{22}{7} \times 14 \times 8 + \frac{22}{7} \times 14 \times 17.5$
$= 1474$ m$^2$
OR
(iii) (b) Volume of air inside the tent
$= \frac{22}{7} \times 14 \times 14 \times 8 + \frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times 10.5$
$= 7084$ m$^3$
Radius of conical part $= 14$ m
Slant height $= \sqrt{(10.5)^2 + (14)^2} = 17.5$ m
(ii) Floor area $= \frac{22}{7} \times 14 \times 14 = 616$ m$^2$
(iii) (a) Area of cloth used
$= 2 \times \frac{22}{7} \times 14 \times 8 + \frac{22}{7} \times 14 \times 17.5$
$= 1474$ m$^2$
OR
(iii) (b) Volume of air inside the tent
$= \frac{22}{7} \times 14 \times 14 \times 8 + \frac{1}{3} \times \frac{22}{7} \times 14 \times 14 \times 10.5$
$= 7084$ m$^3$