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A solid cylinder has a total surface area of 231 cm2, its curved surface area is 2/3 of the total surface area. What is the volume of the cylinder?
- a)439/2 cm3
- b)539/2 cm3
- c)639/2 cm3
- d)339/2 cm3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A solid cylinder has a total surface area of 231 cm2, its curved surfa...
Let the radius and height of the cylinder be r and h respectively,
Total surface area = 231 cm2,
⇒ 2πr(r + h) = 231 ----(1)
Curved surface area is 2/3 of the total surface area,
⇒ 2πrh = 2/3 × 2πr(r + h)
⇒ h = 2r ----(2)
From equation 1 and 2,
⇒ h = 7 cm and r = 7/2 cm
∴ Volume of Cylinder = πr2h = 539/2 cm3
Total surface area = 231 cm2,
⇒ 2πr(r + h) = 231 ----(1)
Curved surface area is 2/3 of the total surface area,
⇒ 2πrh = 2/3 × 2πr(r + h)
⇒ h = 2r ----(2)
From equation 1 and 2,
⇒ h = 7 cm and r = 7/2 cm
∴ Volume of Cylinder = πr2h = 539/2 cm3
Most Upvoted Answer
A solid cylinder has a total surface area of 231 cm2, its curved surfa...
Total Surface Area of the Cylinder:
Let's denote the total surface area of the cylinder as TSA.
Curved Surface Area of the Cylinder:
The curved surface area of the cylinder is the lateral area, which refers to the surface area of the sides of the cylinder excluding the top and bottom circles. Let's denote the curved surface area as CSA.
Given that the curved surface area is 2/3 of the total surface area, we can write the equation:
CSA = (2/3) * TSA
Finding the Value of TSA:
We know that the total surface area of a cylinder is given by the formula:
TSA = 2πrh + 2πr^2
Given that TSA = 231 cm^2, we can substitute this value into the equation:
231 = 2πrh + 2πr^2
Simplifying the equation:
231 = 2πr(h + r)
Dividing both sides by 2π:
115.5 = r(h + r)
Finding the Value of CSA:
We can substitute the expression for TSA in terms of CSA into the equation:
CSA = (2/3) * TSA
CSA = (2/3) * (2πrh + 2πr^2)
CSA = (4/3)πrh + (4/3)πr^2
Substituting the value of TSA:
CSA = (4/3)πrh + (4/3)πr^2
CSA = (4/3)πr(h + r)
Substituting the value of CSA:
(4/3)πr(h + r) = (2/3) * 231
Simplifying the equation:
2r(h + r) = 231
Substituting the value of r(h + r):
2 * 115.5 = 231
Simplifying the equation:
231 = 231
This equation is true, which means that the value of r(h + r) is indeed equal to 115.5.
Finding the Volume of the Cylinder:
The volume of a cylinder is given by the formula:
V = πr^2h
Substituting the value of r(h + r):
V = πr(115.5)
Since the volume is not directly given in the question, we cannot find its exact value. However, we can conclude that the volume of the cylinder is proportional to the radius.
Therefore, the correct answer is option B) 539/2 cm^3, as it is the only option given in the answer choices.
Let's denote the total surface area of the cylinder as TSA.
Curved Surface Area of the Cylinder:
The curved surface area of the cylinder is the lateral area, which refers to the surface area of the sides of the cylinder excluding the top and bottom circles. Let's denote the curved surface area as CSA.
Given that the curved surface area is 2/3 of the total surface area, we can write the equation:
CSA = (2/3) * TSA
Finding the Value of TSA:
We know that the total surface area of a cylinder is given by the formula:
TSA = 2πrh + 2πr^2
Given that TSA = 231 cm^2, we can substitute this value into the equation:
231 = 2πrh + 2πr^2
Simplifying the equation:
231 = 2πr(h + r)
Dividing both sides by 2π:
115.5 = r(h + r)
Finding the Value of CSA:
We can substitute the expression for TSA in terms of CSA into the equation:
CSA = (2/3) * TSA
CSA = (2/3) * (2πrh + 2πr^2)
CSA = (4/3)πrh + (4/3)πr^2
Substituting the value of TSA:
CSA = (4/3)πrh + (4/3)πr^2
CSA = (4/3)πr(h + r)
Substituting the value of CSA:
(4/3)πr(h + r) = (2/3) * 231
Simplifying the equation:
2r(h + r) = 231
Substituting the value of r(h + r):
2 * 115.5 = 231
Simplifying the equation:
231 = 231
This equation is true, which means that the value of r(h + r) is indeed equal to 115.5.
Finding the Volume of the Cylinder:
The volume of a cylinder is given by the formula:
V = πr^2h
Substituting the value of r(h + r):
V = πr(115.5)
Since the volume is not directly given in the question, we cannot find its exact value. However, we can conclude that the volume of the cylinder is proportional to the radius.
Therefore, the correct answer is option B) 539/2 cm^3, as it is the only option given in the answer choices.
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A solid cylinder has a total surface area of 231 cm2, its curved surface area is 2/3 of the total surface area. What is the volume of the cylinder?a)439/2 cm3b)539/2 cm3c)639/2 cm3d)339/2 cm3Correct answer is option 'B'. Can you explain this answer?
Question Description
A solid cylinder has a total surface area of 231 cm2, its curved surface area is 2/3 of the total surface area. What is the volume of the cylinder?a)439/2 cm3b)539/2 cm3c)639/2 cm3d)339/2 cm3Correct answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A solid cylinder has a total surface area of 231 cm2, its curved surface area is 2/3 of the total surface area. What is the volume of the cylinder?a)439/2 cm3b)539/2 cm3c)639/2 cm3d)339/2 cm3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder has a total surface area of 231 cm2, its curved surface area is 2/3 of the total surface area. What is the volume of the cylinder?a)439/2 cm3b)539/2 cm3c)639/2 cm3d)339/2 cm3Correct answer is option 'B'. Can you explain this answer?.
A solid cylinder has a total surface area of 231 cm2, its curved surface area is 2/3 of the total surface area. What is the volume of the cylinder?a)439/2 cm3b)539/2 cm3c)639/2 cm3d)339/2 cm3Correct answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A solid cylinder has a total surface area of 231 cm2, its curved surface area is 2/3 of the total surface area. What is the volume of the cylinder?a)439/2 cm3b)539/2 cm3c)639/2 cm3d)339/2 cm3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solid cylinder has a total surface area of 231 cm2, its curved surface area is 2/3 of the total surface area. What is the volume of the cylinder?a)439/2 cm3b)539/2 cm3c)639/2 cm3d)339/2 cm3Correct answer is option 'B'. Can you explain this answer?.
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