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The curved surface area of a right circular cone is 1.76 m2 and its base diameter is 140 cm. What is the height of the cone?
- a)10 cm
- b)10√2 cm
- c)20√2 cm
- d)10√15 cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The curved surface area of a right circular cone is 1.76 m2and its bas...
Curved surface area of cone = π r l
17600 = 22/7 × 70 × l [∵ 1 m2 = 10000 cm2 and radius = diameter/2]
∴ l = 17600/220 = 80 cm
h = √(l2 - r2)
⇒ √(802 - 702)
⇒ √1500 = 10√15 cm
17600 = 22/7 × 70 × l [∵ 1 m2 = 10000 cm2 and radius = diameter/2]
∴ l = 17600/220 = 80 cm
h = √(l2 - r2)
⇒ √(802 - 702)
⇒ √1500 = 10√15 cm
Most Upvoted Answer
The curved surface area of a right circular cone is 1.76 m2and its bas...
Given Data:
Curved surface area of cone = 1.76 m²
Base diameter = 140 cm
Conversion:
1 cm = 0.01 m
Step 1: Calculating radius of the cone's base
Radius (r) = Diameter / 2
r = 140 cm / 2
r = 70 cm = 0.7 m
Step 2: Calculating slant height of the cone
Curved surface area of cone = π*r*l
1.76 = π*0.7*l
l = 1.76 / (π*0.7)
l ≈ 0.8 m
Step 3: Calculating height of the cone
Using Pythagorean theorem:
l² = r² + h²
0.8² = 0.7² + h²
0.64 = 0.49 + h²
h² = 0.64 - 0.49
h² = 0.15
h = √0.15
h = √(15/100)
h = 0.15√100
h = 0.15*10
h = 1.5 m = 150 cm
Step 4: Converting height to radical form
h = 10√15 cm
Therefore, the height of the cone is 10√15 cm, which matches with option 'D'.
Curved surface area of cone = 1.76 m²
Base diameter = 140 cm
Conversion:
1 cm = 0.01 m
Step 1: Calculating radius of the cone's base
Radius (r) = Diameter / 2
r = 140 cm / 2
r = 70 cm = 0.7 m
Step 2: Calculating slant height of the cone
Curved surface area of cone = π*r*l
1.76 = π*0.7*l
l = 1.76 / (π*0.7)
l ≈ 0.8 m
Step 3: Calculating height of the cone
Using Pythagorean theorem:
l² = r² + h²
0.8² = 0.7² + h²
0.64 = 0.49 + h²
h² = 0.64 - 0.49
h² = 0.15
h = √0.15
h = √(15/100)
h = 0.15√100
h = 0.15*10
h = 1.5 m = 150 cm
Step 4: Converting height to radical form
h = 10√15 cm
Therefore, the height of the cone is 10√15 cm, which matches with option 'D'.
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The curved surface area of a right circular cone is 1.76 m2and its base diameter is 140 cm. What is the height of the cone?a)10 cmb)10√2 cmc)20√2 cmd)10√15 cmCorrect answer is option 'D'. Can you explain this answer?
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The curved surface area of a right circular cone is 1.76 m2and its base diameter is 140 cm. What is the height of the cone?a)10 cmb)10√2 cmc)20√2 cmd)10√15 cmCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The curved surface area of a right circular cone is 1.76 m2and its base diameter is 140 cm. What is the height of the cone?a)10 cmb)10√2 cmc)20√2 cmd)10√15 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The curved surface area of a right circular cone is 1.76 m2and its base diameter is 140 cm. What is the height of the cone?a)10 cmb)10√2 cmc)20√2 cmd)10√15 cmCorrect answer is option 'D'. Can you explain this answer?.
The curved surface area of a right circular cone is 1.76 m2and its base diameter is 140 cm. What is the height of the cone?a)10 cmb)10√2 cmc)20√2 cmd)10√15 cmCorrect answer is option 'D'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The curved surface area of a right circular cone is 1.76 m2and its base diameter is 140 cm. What is the height of the cone?a)10 cmb)10√2 cmc)20√2 cmd)10√15 cmCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The curved surface area of a right circular cone is 1.76 m2and its base diameter is 140 cm. What is the height of the cone?a)10 cmb)10√2 cmc)20√2 cmd)10√15 cmCorrect answer is option 'D'. Can you explain this answer?.
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