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The sum of the radius and height of a cylinder is 18 metre. The total surface area of the cylinder is 792 sq. metre, what is the volume of the cylinder? (in cubic metre)
- a)1848
- b)1440
- c)1716
- d)1724
- e)1694
Correct answer is option 'E'. Can you explain this answer?
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Given:
- Sum of the radius and height of a cylinder = 18 meters.
- Total surface area of the cylinder = 792 sq. meters.
To find:
- Volume of the cylinder.
Formula:
- Total surface area of a cylinder = 2πr(r + h)
- Volume of a cylinder = πr²h
Solution:
Let's assume the radius of the cylinder to be 'r' and the height to be 'h'.
Step 1: Express the given information as equations.
- r + h = 18 (Equation 1)
- 2πr(r + h) = 792 (Equation 2)
Step 2: Solve Equation 1 for 'h'.
- h = 18 - r
Step 3: Substitute the value of 'h' in Equation 2.
- 2πr(r + (18 - r)) = 792
- 2πr(18) = 792
- 36πr = 792
- r = 22/π
Step 4: Substitute the value of 'r' in Equation 1 to find 'h'.
- (22/π) + h = 18
- h = 18 - (22/π)
Step 5: Substitute the values of 'r' and 'h' in the formula to find the volume of the cylinder.
- Volume of the cylinder = π(22/π)²(18 - (22/π))
- Volume of the cylinder = (22/π)²(18 - (22/π))
- Volume of the cylinder = 1694 cubic meters
Therefore, the volume of the cylinder is 1694 cubic meters, which corresponds to option 'E'.
- Sum of the radius and height of a cylinder = 18 meters.
- Total surface area of the cylinder = 792 sq. meters.
To find:
- Volume of the cylinder.
Formula:
- Total surface area of a cylinder = 2πr(r + h)
- Volume of a cylinder = πr²h
Solution:
Let's assume the radius of the cylinder to be 'r' and the height to be 'h'.
Step 1: Express the given information as equations.
- r + h = 18 (Equation 1)
- 2πr(r + h) = 792 (Equation 2)
Step 2: Solve Equation 1 for 'h'.
- h = 18 - r
Step 3: Substitute the value of 'h' in Equation 2.
- 2πr(r + (18 - r)) = 792
- 2πr(18) = 792
- 36πr = 792
- r = 22/π
Step 4: Substitute the value of 'r' in Equation 1 to find 'h'.
- (22/π) + h = 18
- h = 18 - (22/π)
Step 5: Substitute the values of 'r' and 'h' in the formula to find the volume of the cylinder.
- Volume of the cylinder = π(22/π)²(18 - (22/π))
- Volume of the cylinder = (22/π)²(18 - (22/π))
- Volume of the cylinder = 1694 cubic meters
Therefore, the volume of the cylinder is 1694 cubic meters, which corresponds to option 'E'.
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The sum of the radius and height of a cylinder is 18 metre. The total surface area of the cylinder is 792 sq. metre, what is the volume of the cylinder? (in cubic metre)a)1848b)1440c)1716d)1724e)1694Correct answer is option 'E'. Can you explain this answer?
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The sum of the radius and height of a cylinder is 18 metre. The total surface area of the cylinder is 792 sq. metre, what is the volume of the cylinder? (in cubic metre)a)1848b)1440c)1716d)1724e)1694Correct answer is option 'E'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The sum of the radius and height of a cylinder is 18 metre. The total surface area of the cylinder is 792 sq. metre, what is the volume of the cylinder? (in cubic metre)a)1848b)1440c)1716d)1724e)1694Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the radius and height of a cylinder is 18 metre. The total surface area of the cylinder is 792 sq. metre, what is the volume of the cylinder? (in cubic metre)a)1848b)1440c)1716d)1724e)1694Correct answer is option 'E'. Can you explain this answer?.
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