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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.

Answer:

**Solution:**

For finding the area of canvas used for making the tent made up of combination of cone and cylinder , we need to add curved surface area of both.

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 = √(h^{2}+r^{2})

*l* = √(5^{2}+12^{2})

*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

= 2π rH+π r*l*

= π r(2H+*l*)

= (22/7)×12×(2×11+13)

= (264/7)×(22+13)

= (264/7)×35

= 264×5

= 1320 m^{2}

**Hence the area of canvas used to make the tent is 1320 m ^{2} .**

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