Q) A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, find the area of the canvas required for making the tent, keeping a provision of 26 m² of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of 500 per m².

Ans:

A tent is in the shape of a cylinder surmounted CBSE 10th board Sample paper 2023 Important questions

Here, in this question, it is given that:

Height of total shape = 13.5 m, height of cylindrical shape = 3 m,

Therefore, height of the canonical top = 13.5 – 3 = 10.5 m

Radius of the model = 14 m,

Therefore, slant height of the canonical top = \sqrt{(14)^2 + (10.5)^2} = \sqrt {306.25} = 17.5 m

Curved surface area of canonical top = \pi (r) (l)

= (\frac{22}{7}) (14)(17.5) = 770 m2 …….. (i)

Curved surface area of cylindrical base = 2 \pi (r) (h)

= 2 x (\frac{22}{7}) (14)(3) = 264 m2 ……….. (ii)

Therefore, Curved surface Area of tent = 770 + 264 = 1034 m2

It is given that a provision of 26 mis required, Therefore, Area of the canvas required to make this tent = 1034 + 26 = 1060 m2

Since the cost of canvas = Rs. 500 / m2

Therefore, the cost of the canvas = 1060 x 500 = Rs. 530,000

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