M.L Aggarwal book Important Question of class 10 chapter Based on Mensuration for ICSE BOARD.
A circus tent is in the shape of a cylinder surmounted by a cone. The diameter of the cylindrical portion and its height is given. If the vertex of the cone is 16 m above the ground, find the area of the canvas used to make the tent.
This is the Question Number 10, Exercise 17.4 of M.L Aggarwal.
Deepak BoraNewbie
A circus tent is in the shape of a cylinder surmounted by a cone. The diameter of the cylindrical portion is 24 m and its height is 11 m. If the vertex of the cone is 16 m above the ground, find the area of the canvas used to make the tent.
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Given diameter of the cylindrical part of tent, d = 24 m
Radius, r = d/2 = 24/2 = 12 m
Height of the cylindrical part, H = 11 m
Since vertex of cone is 16 m above the ground, height of cone, h = 16-11
h = 5 m
Slant height of the cone, l = √(h2+r2)
l = √(52+122)
l = √(25+144)
l = √(169)
l = 13 m
Radius of cone, r = 12 m
Area of canvas used to make the tent = curved surface area of the cylindrical part + curved surface area of the cone.
Area of canvas used to make the tent = 2rH+rl
= r(2H+l)
= (22/7)×12×(2×11+13)
= (264/7)×(22+13)
= (264/7)×35
= 264×5
= 1320 m2
Hence the area of canvas used to make the tent is 1320 m2 .