Question

Q. Meera has a piece of canvas whose area is 551 m². She uses it to have a conical tent made, with a base radius of 7 m. Assuming that all the stitching margins and the wastage incurred while cutting, amounts to approximately 1 m² find the volume of the tent that can be made with it.


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Answer 1

Step-by-step explanation:

Let Tent have Radius = r = 7m

Let slant height = l m

let height = h m

Area of canvas = area available for making tent + wastage 551 m² = area available for maing tent + 1 m² area available for making tent = 551 m² - 1 m² = 550 m²

Area available for making tent = Curved surface area of conical tent 550 = πrl

550 = 22 × 1 × l

22 × 1 × l = 550

l = 550/22 m

l = 25 m

we know that

l² = h²+ r²

25² = h² + 7²

25² - 7² = h²

h² = 25² - 7²

h² = (25 - 7) (25 + 7)

h² = (18) (32)

h =√18(32)

h = √(9 × 2) × (32)

h =√(9) × (64)

h = √(3²) × (8²)

h = 3 × 8

h = 24 m

volume of tent = 1/3πr²h

= 1/3 × 22/7 × 7 × 7 × 24 m³

= 22 × 1 × 7 × 8 m³

= 1232 m³