Question

A tank is in the shape of the cylinders surmounted by a conical top if the height and the diameter of the cylindrical part are 2.1 m and 4m respectively and the slant height of the top is 2.8 m find the area of the Canvas used for making the tent . also the cost of the Canvas of the tent at the rupees 500 per m² ( note that the base of the tent will not be covered with Canvas) ?

Answer 1

Solution: Radius of cylinder = 2 m, height = 2.1 m and slant height of conical top = 2.8 m

Curved Surface Area of cylindrical portion

=2πrh=2πrh
=2π×2×2.1=8π m2=2π×2×2.1=8π m2

Curved Surface Area of conical portion

=πrl=πrl
=π×2×2.8=5.6π m2=π×2×2.8=5.6π m2

Total CSA

=8.4π+5.6π=8.4π+5.6π
=14×227=44 m2=14×227=44 m2

Cost of canvas=Rate×Surface AreaCost of canvas=Rate×Surface Area

=500×44=Rs.22000

Answer 2

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From the question, we know that

The diameter = D = 4 m

l = 2.8 m (slant height)

The radius of the cylinder is equal to the radius of the cylinder

So, r = 4/2 = 2 m

Also, we know the height of the cylinder (h) is 2.1 m

So, the required surface area of the given tent = surface area of the cone (the top) + surface area of the cylinder(the base)

= πrl + 2πrh

= πr (l+2h)

Now, substituting the values and solving it we get the value as 44 m^2

∴ The cost of the canvas at the rate of Rs. 500 per m^2 for the tent will be

= Surface area × cost/ m^2

= 44 × 500

So, Rs. 22000 will be the total cost of the canvas

Hope it's Helpful.....:)