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The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.
- a)3 : 7
- b)7 : 3
- c)6 : 7
- d)7 : 6
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The curved surface area of a cylindrical pillar is 264 m2 and its volu...
(πr2h)/ (2πrh) = 924/264
r = [(924 /264) × 2] = 7 m and, 2πrh = 264
h = (264 × 7/22 × 1/2 × 1/7) = 6 m
∴ Required ratio = 2r/h =14/6 = 7 : 3
r = [(924 /264) × 2] = 7 m and, 2πrh = 264
h = (264 × 7/22 × 1/2 × 1/7) = 6 m
∴ Required ratio = 2r/h =14/6 = 7 : 3
Most Upvoted Answer
The curved surface area of a cylindrical pillar is 264 m2 and its volu...
Given information:
Curved surface area of the cylindrical pillar = 264 m²
Volume of the cylindrical pillar = 924 m³
To find:
Ratio of diameter to height
Formulae:
Curved surface area of a cylinder = 2πrh
Volume of a cylinder = πr²h
Let's solve the problem step by step:
1. Finding the radius:
We know that the curved surface area of a cylinder is given by the formula 2πrh.
Given that the curved surface area is 264 m², we can equate the formula to the given value:
2πrh = 264
2. Finding the height in terms of the radius:
From the formula for volume of a cylinder, we have:
Volume = πr²h
Given that the volume is 924 m³, we can equate the formula to the given value:
πr²h = 924
3. Expressing height in terms of the radius:
From the second equation, we can express the height in terms of the radius:
h = 924 / (πr²)
4. Substituting the value of h in the first equation:
Now, substitute the value of h in terms of the radius (from step 3) into the first equation:
2πr(924 / (πr²)) = 264
5. Simplifying the equation:
Simplify the equation by canceling out π and multiplying through by r:
2 * 924 / r = 264
6. Solving for r:
Solve the equation for r:
r = (2 * 924) / (264)
r = 7
7. Finding the diameter:
The diameter (d) of a cylinder is twice the radius (r):
d = 2 * r
d = 2 * 7
d = 14
8. Finding the height:
Substitute the value of r (from step 6) into the equation for height (from step 3):
h = 924 / (π(7)²)
h ≈ 924 / (154)
h ≈ 6
9. Finding the ratio:
The ratio of diameter to height is given by d:h or 14:6, which simplifies to 7:3.
Therefore, the correct answer is option B) 7:3.
Curved surface area of the cylindrical pillar = 264 m²
Volume of the cylindrical pillar = 924 m³
To find:
Ratio of diameter to height
Formulae:
Curved surface area of a cylinder = 2πrh
Volume of a cylinder = πr²h
Let's solve the problem step by step:
1. Finding the radius:
We know that the curved surface area of a cylinder is given by the formula 2πrh.
Given that the curved surface area is 264 m², we can equate the formula to the given value:
2πrh = 264
2. Finding the height in terms of the radius:
From the formula for volume of a cylinder, we have:
Volume = πr²h
Given that the volume is 924 m³, we can equate the formula to the given value:
πr²h = 924
3. Expressing height in terms of the radius:
From the second equation, we can express the height in terms of the radius:
h = 924 / (πr²)
4. Substituting the value of h in the first equation:
Now, substitute the value of h in terms of the radius (from step 3) into the first equation:
2πr(924 / (πr²)) = 264
5. Simplifying the equation:
Simplify the equation by canceling out π and multiplying through by r:
2 * 924 / r = 264
6. Solving for r:
Solve the equation for r:
r = (2 * 924) / (264)
r = 7
7. Finding the diameter:
The diameter (d) of a cylinder is twice the radius (r):
d = 2 * r
d = 2 * 7
d = 14
8. Finding the height:
Substitute the value of r (from step 6) into the equation for height (from step 3):
h = 924 / (π(7)²)
h ≈ 924 / (154)
h ≈ 6
9. Finding the ratio:
The ratio of diameter to height is given by d:h or 14:6, which simplifies to 7:3.
Therefore, the correct answer is option B) 7:3.
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The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.a)3 : 7b)7 : 3c)6 : 7d)7 : 6Correct answer is option 'B'. Can you explain this answer?
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The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.a)3 : 7b)7 : 3c)6 : 7d)7 : 6Correct answer is option 'B'. Can you explain this answer? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.a)3 : 7b)7 : 3c)6 : 7d)7 : 6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.a)3 : 7b)7 : 3c)6 : 7d)7 : 6Correct answer is option 'B'. Can you explain this answer?.
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