Question

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 stitching . Also find the cost of canvas at the rate of ₹ 80 per metre.​

Answer 1

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Given:

Canvas of width 2m

To make conical tent of diameter 20m and 42 m in slant height

10% extra cloth for folds and stitching

Cost of canvas is Rs 80 per meter

To find:

1. Length of canvas required to make conical tent = ?
2. Cost of canvas = ?

Solution:

We have to find Surface area of conical tent to find area of canvas required

Diameter = 20 m

Radius = Diameter/2 = 20/2 = 10 m

Slant height = L = 42 m

Value of π = 22/7 or 3.14

Surface area of cone = Curved surface area of cone + area of base

Surface area (SA) = πrL + πr²

SA = 22/7 × 10 × 42 + 22/7 × 10 × 10

SA = 1320 + 2200/7

SA = 1320 + 314.28

SA = 1634.2 m²

10% extra cloth = 10/100 × 1634.2

= 163.42 m²

Total canvas required = 1634.2 + 163.42

= 1797.62 m²

As canvas is like a rectangular cloth,

Area = length × width

Length = Area / Width

Length = 1797.62/2

Length = 898.81 m

Cost of 1 meter canvas cost Rs 80

Cost of 898.81 meter canvas cost

= 898.81 × 80/1

= Rs 71904.8

Required answer:

Thus, 898.81 m canvas is required to make conical tent and cost of canvas is Rs 71904.8