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# 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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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.

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1. 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)

= √(52+122)

= √(25+144)

= √(169)

= 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 .

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