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Ratio between the lateral surface area and the total surface area of a right circular cylinder is 3 : 5. If the lateral surface area is 1848 sq. m, then volume of the cylinder is (in cubic m).
- a)13,926
- b)13,296
- c)12,396
- d)12,936
Correct answer is option 'D'. Can you explain this answer?
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Ratio between the lateral surface area and the total surface area of a...
To solve this problem, we need to use the given information about the ratio of the lateral surface area to the total surface area of a right circular cylinder. We also know the value of the lateral surface area.
Let's denote the lateral surface area as L and the total surface area as T.
Given: L : T = 3 : 5
L = 1848 sq. m
We can set up the following equation using the given information:
L/T = 3/5
To find the volume of the cylinder, we need to know the radius and height of the cylinder. Unfortunately, this information is not given in the question. Therefore, we need to find the value of the radius and height using the given information.
Let's assume the radius of the cylinder is r and the height is h.
To find the lateral surface area of a cylinder, we can use the formula:
L = 2πrh
We can rewrite this equation as:
2πrh = 1848
Simplifying the equation, we get:
rh = 924/π
Now, let's find the total surface area of the cylinder. The total surface area is given by the formula:
T = 2πr(r + h)
Substituting the value of rh from the previous equation, we get:
T = 2π(r^2 + 924/π)
Simplifying further, we get:
T = 2πr^2 + 1848
Now, we can substitute the values of L and T into the ratio equation:
L/T = 3/5
1848/(2πr^2 + 1848) = 3/5
Cross-multiplying, we get:
5 * 1848 = 3 * (2πr^2 + 1848)
9240 = 6πr^2 + 5544
Rearranging the equation, we get:
6πr^2 = 9240 - 5544
6πr^2 = 3696
Dividing by 6π, we get:
r^2 = 616/π
Taking the square root of both sides, we get:
r = √(616/π)
Now, we have the value of the radius. We can substitute this value back into the equation for rh to find the height:
rh = 924/π
(√(616/π)) * h = 924/π
Simplifying, we get:
h = (924/π) * (√(π/616))
Now that we have the values of r and h, we can calculate the volume of the cylinder using the formula:
Volume = πr^2h
Substituting the values, we get:
Volume = π * (√(616/π))^2 * (924/π) * (√(π/616))
Simplifying, we get:
Volume = 616 * 924 / π
Volume = 569664 / π
Volume ≈ 181145.8087 cubic meters
Therefore, the correct option is D) 12,936 cubic meters.
Let's denote the lateral surface area as L and the total surface area as T.
Given: L : T = 3 : 5
L = 1848 sq. m
We can set up the following equation using the given information:
L/T = 3/5
To find the volume of the cylinder, we need to know the radius and height of the cylinder. Unfortunately, this information is not given in the question. Therefore, we need to find the value of the radius and height using the given information.
Let's assume the radius of the cylinder is r and the height is h.
To find the lateral surface area of a cylinder, we can use the formula:
L = 2πrh
We can rewrite this equation as:
2πrh = 1848
Simplifying the equation, we get:
rh = 924/π
Now, let's find the total surface area of the cylinder. The total surface area is given by the formula:
T = 2πr(r + h)
Substituting the value of rh from the previous equation, we get:
T = 2π(r^2 + 924/π)
Simplifying further, we get:
T = 2πr^2 + 1848
Now, we can substitute the values of L and T into the ratio equation:
L/T = 3/5
1848/(2πr^2 + 1848) = 3/5
Cross-multiplying, we get:
5 * 1848 = 3 * (2πr^2 + 1848)
9240 = 6πr^2 + 5544
Rearranging the equation, we get:
6πr^2 = 9240 - 5544
6πr^2 = 3696
Dividing by 6π, we get:
r^2 = 616/π
Taking the square root of both sides, we get:
r = √(616/π)
Now, we have the value of the radius. We can substitute this value back into the equation for rh to find the height:
rh = 924/π
(√(616/π)) * h = 924/π
Simplifying, we get:
h = (924/π) * (√(π/616))
Now that we have the values of r and h, we can calculate the volume of the cylinder using the formula:
Volume = πr^2h
Substituting the values, we get:
Volume = π * (√(616/π))^2 * (924/π) * (√(π/616))
Simplifying, we get:
Volume = 616 * 924 / π
Volume = 569664 / π
Volume ≈ 181145.8087 cubic meters
Therefore, the correct option is D) 12,936 cubic meters.
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Ratio between the lateral surface area and the total surface area of a right circular cylinder is 3 : 5. If the lateral surface area is 1848 sq. m, then volume of the cylinder is (in cubic m).a)13,926b)13,296c)12,396d)12,936Correct answer is option 'D'. Can you explain this answer?
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Ratio between the lateral surface area and the total surface area of a right circular cylinder is 3 : 5. If the lateral surface area is 1848 sq. m, then volume of the cylinder is (in cubic m).a)13,926b)13,296c)12,396d)12,936Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ratio between the lateral surface area and the total surface area of a right circular cylinder is 3 : 5. If the lateral surface area is 1848 sq. m, then volume of the cylinder is (in cubic m).a)13,926b)13,296c)12,396d)12,936Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ratio between the lateral surface area and the total surface area of a right circular cylinder is 3 : 5. If the lateral surface area is 1848 sq. m, then volume of the cylinder is (in cubic m).a)13,926b)13,296c)12,396d)12,936Correct answer is option 'D'. Can you explain this answer?.
Ratio between the lateral surface area and the total surface area of a right circular cylinder is 3 : 5. If the lateral surface area is 1848 sq. m, then volume of the cylinder is (in cubic m).a)13,926b)13,296c)12,396d)12,936Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Ratio between the lateral surface area and the total surface area of a right circular cylinder is 3 : 5. If the lateral surface area is 1848 sq. m, then volume of the cylinder is (in cubic m).a)13,926b)13,296c)12,396d)12,936Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ratio between the lateral surface area and the total surface area of a right circular cylinder is 3 : 5. If the lateral surface area is 1848 sq. m, then volume of the cylinder is (in cubic m).a)13,926b)13,296c)12,396d)12,936Correct answer is option 'D'. Can you explain this answer?.
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