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.

Share

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,Â

lÂ = âˆš(h^{2}+r^{2})lÂ= âˆš(5^{2}+12^{2})lÂ= âˆš(25+144)lÂ= âˆš(169)lÂ= 13 mRadius 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+r

l= r(2H+

l)= (22/7)Ã—12Ã—(2Ã—11+13)

= (264/7)Ã—(22+13)

= (264/7)Ã—35

= 264Ã—5

= 1320 m

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

^{2}Â .