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The radius of the base and height of a solid cylinder are in the ratio 2 ∶ 3 and its volume is 1617 cm3. What is the total surface area of the cylinder?
- a)462 cm2
- b)616 cm2
- c)770 cm2
- d)786 cm2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The radius of the base and height of a solid cylinder are in the ratio...
Ratio of radius of the base and height = 2 ∶ 3;
Let the radius and height be 2x and 3x respectively;
Given that volume is 1617 cm3;
⇒ πr2h = 1617
⇒ (22/7) × 4x2 × 3x = 1617
⇒ x3 = 42.875
⇒ x = 3.5 cm
⇒ Radius = 7 cm and Height = 10.5 cm;
∴ Total surface area of the cylinder = (2πr2 + 2πrh)
⇒ 2 × 22/7 × (72 + 7 × 10.5)
⇒ 770 cm2
Let the radius and height be 2x and 3x respectively;
Given that volume is 1617 cm3;
⇒ πr2h = 1617
⇒ (22/7) × 4x2 × 3x = 1617
⇒ x3 = 42.875
⇒ x = 3.5 cm
⇒ Radius = 7 cm and Height = 10.5 cm;
∴ Total surface area of the cylinder = (2πr2 + 2πrh)
⇒ 2 × 22/7 × (72 + 7 × 10.5)
⇒ 770 cm2
Most Upvoted Answer
The radius of the base and height of a solid cylinder are in the ratio...
Understanding the Problem
To solve the problem, we need to find the total surface area of a solid cylinder given the volume and the ratio of its dimensions.
Given Data
- Volume of the cylinder (V) = 1617 cm³
- Ratio of radius (r) to height (h) = 2:3
Calculating Radius and Height
1. Let the radius be 2x and height be 3x:
- r = 2x
- h = 3x
2. Volume formula for a cylinder:
- V = πr²h
3. Substituting the values:
- 1617 = π(2x)²(3x)
- Simplifying gives:
- 1617 = 12πx³
- x³ = 1617 / (12π)
- x³ ≈ 42.75
- x ≈ 3.5 (taking the cube root)
4. Calculating r and h:
- r = 2x = 2 * 3.5 = 7 cm
- h = 3x = 3 * 3.5 = 10.5 cm
Calculating Total Surface Area
1. Total surface area (A) formula:
- A = 2πr(h + r)
2. Substituting values:
- A = 2π(7)(10.5 + 7)
- A = 2π(7)(17.5)
- A = 245π
3. Approximating π = 3.14:
- A ≈ 245 * 3.14 ≈ 770 cm²
Final Result
Thus, the total surface area of the cylinder is approximately 770 cm², which corresponds to option 'C'.
To solve the problem, we need to find the total surface area of a solid cylinder given the volume and the ratio of its dimensions.
Given Data
- Volume of the cylinder (V) = 1617 cm³
- Ratio of radius (r) to height (h) = 2:3
Calculating Radius and Height
1. Let the radius be 2x and height be 3x:
- r = 2x
- h = 3x
2. Volume formula for a cylinder:
- V = πr²h
3. Substituting the values:
- 1617 = π(2x)²(3x)
- Simplifying gives:
- 1617 = 12πx³
- x³ = 1617 / (12π)
- x³ ≈ 42.75
- x ≈ 3.5 (taking the cube root)
4. Calculating r and h:
- r = 2x = 2 * 3.5 = 7 cm
- h = 3x = 3 * 3.5 = 10.5 cm
Calculating Total Surface Area
1. Total surface area (A) formula:
- A = 2πr(h + r)
2. Substituting values:
- A = 2π(7)(10.5 + 7)
- A = 2π(7)(17.5)
- A = 245π
3. Approximating π = 3.14:
- A ≈ 245 * 3.14 ≈ 770 cm²
Final Result
Thus, the total surface area of the cylinder is approximately 770 cm², which corresponds to option 'C'.
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The radius of the base and height of a solid cylinder are in the ratio 2 ∶3 and its volume is 1617 cm3. What is the total surface area of the cylinder?a)462 cm2b)616 cm2c)770 cm2d)786 cm2Correct answer is option 'C'. Can you explain this answer?
Question Description
The radius of the base and height of a solid cylinder are in the ratio 2 ∶3 and its volume is 1617 cm3. What is the total surface area of the cylinder?a)462 cm2b)616 cm2c)770 cm2d)786 cm2Correct answer is option 'C'. 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 radius of the base and height of a solid cylinder are in the ratio 2 ∶3 and its volume is 1617 cm3. What is the total surface area of the cylinder?a)462 cm2b)616 cm2c)770 cm2d)786 cm2Correct answer is option 'C'. 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 radius of the base and height of a solid cylinder are in the ratio 2 ∶3 and its volume is 1617 cm3. What is the total surface area of the cylinder?a)462 cm2b)616 cm2c)770 cm2d)786 cm2Correct answer is option 'C'. Can you explain this answer?.
The radius of the base and height of a solid cylinder are in the ratio 2 ∶3 and its volume is 1617 cm3. What is the total surface area of the cylinder?a)462 cm2b)616 cm2c)770 cm2d)786 cm2Correct answer is option 'C'. 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 radius of the base and height of a solid cylinder are in the ratio 2 ∶3 and its volume is 1617 cm3. What is the total surface area of the cylinder?a)462 cm2b)616 cm2c)770 cm2d)786 cm2Correct answer is option 'C'. 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 radius of the base and height of a solid cylinder are in the ratio 2 ∶3 and its volume is 1617 cm3. What is the total surface area of the cylinder?a)462 cm2b)616 cm2c)770 cm2d)786 cm2Correct answer is option 'C'. Can you explain this answer?.
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