A military tent of height 8.25 m is in the form of a right circular cylinder of base diameter 30 m and height 5.5 m surmounted by a right circular cone of same base radius. Find the length of canvas used in making the tent, if the breadth of the canvas is 1.5 m

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This question is combination of cone and cylinder by using there surface area and volume formulas we will get required parameter’s. Volume and surface area of solids from RS Aggarwal book exercise 17A, page number 787 problem number 9

Total Height of tent = h = 8.25 m

Base diameter of tent = 30 m,

then

Base radius of tent = r = 30/2 m = 15 m

Height of right circular cylinder = 5.5 m

Base radius of cone = 15 m

Let slant height of cone = l m

Now,

Curved surface area of right circular cylindrical part of tent = 2πrh

and

Height of conical part = total height of tent – height of cylindrical part

Height of cone = 8.25 – 5.5 = 2.75 m

Using Pythagoras Ther0m

l

^{2}= h^{2}+ r^{2}= 2.75

^{2}+ 15^{2}= 232.5625

or l = 15.25 m

Curved surface area of conical part of the tent = πrl

Total surface area of the tent = Curved surface area of cylindrical part + curved surface area of conical part

Total surface area of tent = 2πrh + πrl

= πr(2h + l)

= 22/7 × 15 × (2 × 5

= 1237.5

Total surface area of tent is 1237.5 m

^{2}Breadth of canvas used = 1.5 m

Length of canvas used x breadth of canvas used = Total surface area of tent

Length of canvas used = 1237.51.5 = 825

∴ Length of canvas used is 825 m