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Find what length of canvas 2 m in width is required to make a conical tent 20 m in diameter and 42 m in slant height allowing 10% for folds and the stitching. Also find the cost of the canvas at the rate of Rs 80 per metre.

Answer:

**Solution:**

The portion of a cone not including the base is considered as its curved surface. In other words, it is the portion of the cone that is visible when it is unfolded.

Given diameter of the conical tent, d = 20 m

radius, r = d/2 = 20/2 = 10 m

Slant height, l = 42 m

Curved surface area of the conical tent = π r*l*

= (22/7)×10×42

= 22×10×6

= 1320 m^{2}

So the area of canvas required is 1320 m^{2}.

Since 10% of this area is used for folds and stitches, actual cloth needed = 1320+ 10% of 1320

= 1320 + (10/100)×1320

= 1320+132

= 1452 m^{2}

Width of the cloth = 2m

Length of the cloth = Area/width = 1452/2 = 726 m

Cost of canvas = Rs.80 per metre.

Total cost = 80×726 = Rs. 58080

**Hence the total cost of the canvas is Rs. 58080.**

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