Mensuration-10

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A tent is in the form of a cylinder surmounted by a cone. Its diameter is 10.5 m.
The height of the cylindrical portion is 4 m and the greatest height
of the tent is 6.5 m.
Find the volume of air in cubic meters. What is the area of
the canvas required to make the tent?

Solution:Radius of the cylinder = 10.5/2 = 5.25 m

Volume of the cylinder = π r2 h

= 22/7 x 5.25 x 5.25 x 4 cu.m

= 22/7 x 5.25 x 21 = 346.5 cu.m

Volume of the conical part

= π r2 h/3 = 1/3 x 22/7 x 5.25 x 5.25 x 2.5

= 72.1875 cu.m

Volume of the air in the tent = volume of the conical part + volume of the cylindrical part

= (346.5 + 72.1875) cu. m

= 418.6875 cu. m

Slant height of the conical part = l = √(h2 + r2)

= π(2.52 + 5.252) = π(6.25 + 27.5625)

= π(33.8125) = 5.81 (approximately)

Curved surface area of the cone = π r l = 22/7 x 5.25 x 5.81 sq.m

= 95.865 sq. m

Curved surface area of the cylindrical part = 2 π r h

= 2 x 22/7 x 5.25 x 4 = 132 sq. m

Area of canvas required = 132 + 95.865 sq. m = 227.865 sq. m

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