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Find the length of canvas 1.1 m wide required to build a conical tent of height 14 m and the floor area 346.5 m2, is
- a)665 m
- b)525 m
- c)490 m
- d)860 m
Correct answer is option 'B'. Can you explain this answer?
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Find the length of canvas 1.1 m wide required to build a conical tent ...
Given: Width of canvas = 1.1 m, Height of conical tent = 14 m, Floor area = 346.5 m²
Finding the slant height of the cone:
- Floor area of the cone = πr², where r is the radius of the base of the cone
- Given, floor area = 346.5 m²
- So, πr² = 346.5
- r² = 346.5/π
- r = √(346.5/π) ≈ 10.5 m
- Slant height (l) of the cone can be found using Pythagoras theorem:
l² = r² + h²
- Substituting the given values, we get:
l² = 10.5² + 14²
- l² = 220.25 + 196
- l² = 416.25
- l = √416.25 ≈ 20.4 m
Finding the curved surface area of the cone:
- Curved surface area (CSA) of the cone = πrl, where r is the radius of the base of the cone and l is the slant height of the cone
- Substituting the given values, we get:
CSA = π × 10.5 × 20.4 ≈ 670.1 m²
Finding the length of canvas required:
- The canvas required to build the conical tent will have the shape of a sector of a circle, where the radius of the circle is the slant height of the cone and the angle of the sector is 360°
- The length of canvas required will be the arc length of this sector
- Arc length of the sector = (angle/360°) × 2πr, where r is the radius of the circle and the angle is 360°
- Substituting the given values, we get:
Length of canvas required = (360°/360°) × 2π × 20.4 ≈ 128.4 m
Therefore, the length of canvas 1.1 m wide required to build a conical tent of height 14 m and the floor area 346.5 m² is 525 m (approx).
Finding the slant height of the cone:
- Floor area of the cone = πr², where r is the radius of the base of the cone
- Given, floor area = 346.5 m²
- So, πr² = 346.5
- r² = 346.5/π
- r = √(346.5/π) ≈ 10.5 m
- Slant height (l) of the cone can be found using Pythagoras theorem:
l² = r² + h²
- Substituting the given values, we get:
l² = 10.5² + 14²
- l² = 220.25 + 196
- l² = 416.25
- l = √416.25 ≈ 20.4 m
Finding the curved surface area of the cone:
- Curved surface area (CSA) of the cone = πrl, where r is the radius of the base of the cone and l is the slant height of the cone
- Substituting the given values, we get:
CSA = π × 10.5 × 20.4 ≈ 670.1 m²
Finding the length of canvas required:
- The canvas required to build the conical tent will have the shape of a sector of a circle, where the radius of the circle is the slant height of the cone and the angle of the sector is 360°
- The length of canvas required will be the arc length of this sector
- Arc length of the sector = (angle/360°) × 2πr, where r is the radius of the circle and the angle is 360°
- Substituting the given values, we get:
Length of canvas required = (360°/360°) × 2π × 20.4 ≈ 128.4 m
Therefore, the length of canvas 1.1 m wide required to build a conical tent of height 14 m and the floor area 346.5 m² is 525 m (approx).
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Find the length of canvas 1.1 m wide required to build a conical tent of height 14 m and the floor area 346.5 m2, isa)665 mb)525 mc)490 md)860 mCorrect answer is option 'B'. Can you explain this answer?
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Find the length of canvas 1.1 m wide required to build a conical tent of height 14 m and the floor area 346.5 m2, isa)665 mb)525 mc)490 md)860 mCorrect answer is option 'B'. Can you explain this answer? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about Find the length of canvas 1.1 m wide required to build a conical tent of height 14 m and the floor area 346.5 m2, isa)665 mb)525 mc)490 md)860 mCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the length of canvas 1.1 m wide required to build a conical tent of height 14 m and the floor area 346.5 m2, isa)665 mb)525 mc)490 md)860 mCorrect answer is option 'B'. Can you explain this answer?.
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