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Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?
- a)616 cm3
- b)2464 cm3
- c)3672 cm3
- d)1232 cm3
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Ratio of the breadth and length of the rectangle is 7:11 cm and the b...
2 * (7x + 11x) = 72
X = 2
Breadth of the rectangle = 2 * 7 = 14 cm
Height of the cylinder = 14 – 8 = 6 cm
1760 = 2 * 22/7 * r * (r + 6)
r = 14 cm
r2 +6r -280 = 0
r2 +20r -14r -280 = 0
r = 14, -20 (negative value are neglected)
Height of the cone = 11 * 2 + 2 = 24 cm
Radius of the cone = 14/2 = 7 cm
Volume of the cone = 1/3 * 22/7 * 7 * 7 * 24= 1232
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Ratio of the breadth and length of the rectangle is 7:11 cm and the b...
Given information:
- Ratio of breadth and length of the rectangle = 7:11
- Breadth of the rectangle = height of the cylinder + 8 cm
- Total surface area of the cylinder = 1760 cm^2
- Height of the cone = length of the rectangle + 2 cm
- Radius of the cone = half of the radius of the cylinder
- Perimeter of the rectangle = 72 cm
To find: Volume of the cone
Let's solve the problem step by step:
1. Finding the dimensions of the rectangle:
Let's assume the ratio of breadth and length of the rectangle as 7x and 11x respectively.
The perimeter of the rectangle is given as 72 cm, so we can write the equation as follows:
2(7x + 11x) = 72
18x = 36
x = 2
Therefore, the breadth of the rectangle = 7x = 7 * 2 = 14 cm
The length of the rectangle = 11x = 11 * 2 = 22 cm
2. Finding the dimensions of the cylinder:
The breadth of the rectangle is given as 8 cm more than the height of the cylinder.
So, height of the cylinder = breadth of the rectangle - 8 = 14 - 8 = 6 cm
3. Finding the dimensions of the cone:
The height of the cone is given as the length of the rectangle + 2 cm.
So, height of the cone = length of the rectangle + 2 = 22 + 2 = 24 cm
The radius of the cone is given as half of the radius of the cylinder.
Let the radius of the cylinder be r cm.
So, radius of the cone = r/2 cm
4. Finding the volume of the cone:
The formula for the volume of a cone is:
Volume = (1/3) * π * r^2 * h
Substituting the values:
Volume = (1/3) * π * (r/2)^2 * 24
= (1/3) * π * (r^2/4) * 24
= (1/12) * π * r^2 * 24
= 2π * r^2 cm^3
5. Finding the value of r:
The total surface area of the cylinder is given as 1760 cm^2.
The formula for the total surface area of a cylinder is:
Total Surface Area = 2π * r * (r + h)
Substituting the values:
1760 = 2π * r * (r + 6)
880 = π * r * (r + 6)
r^2 + 6r - 880/π = 0
Solving the quadratic equation, we get:
r ≈ 15.4 cm
6. Finding the volume of the cone:
Substituting the value of r in the volume formula, we get:
Volume = 2π * (15.4)^2 cm^3
≈ 1232 cm^3
Therefore, the volume of the cone is approximately 1232 cm^3. Hence, the correct answer is option D.
- Ratio of breadth and length of the rectangle = 7:11
- Breadth of the rectangle = height of the cylinder + 8 cm
- Total surface area of the cylinder = 1760 cm^2
- Height of the cone = length of the rectangle + 2 cm
- Radius of the cone = half of the radius of the cylinder
- Perimeter of the rectangle = 72 cm
To find: Volume of the cone
Let's solve the problem step by step:
1. Finding the dimensions of the rectangle:
Let's assume the ratio of breadth and length of the rectangle as 7x and 11x respectively.
The perimeter of the rectangle is given as 72 cm, so we can write the equation as follows:
2(7x + 11x) = 72
18x = 36
x = 2
Therefore, the breadth of the rectangle = 7x = 7 * 2 = 14 cm
The length of the rectangle = 11x = 11 * 2 = 22 cm
2. Finding the dimensions of the cylinder:
The breadth of the rectangle is given as 8 cm more than the height of the cylinder.
So, height of the cylinder = breadth of the rectangle - 8 = 14 - 8 = 6 cm
3. Finding the dimensions of the cone:
The height of the cone is given as the length of the rectangle + 2 cm.
So, height of the cone = length of the rectangle + 2 = 22 + 2 = 24 cm
The radius of the cone is given as half of the radius of the cylinder.
Let the radius of the cylinder be r cm.
So, radius of the cone = r/2 cm
4. Finding the volume of the cone:
The formula for the volume of a cone is:
Volume = (1/3) * π * r^2 * h
Substituting the values:
Volume = (1/3) * π * (r/2)^2 * 24
= (1/3) * π * (r^2/4) * 24
= (1/12) * π * r^2 * 24
= 2π * r^2 cm^3
5. Finding the value of r:
The total surface area of the cylinder is given as 1760 cm^2.
The formula for the total surface area of a cylinder is:
Total Surface Area = 2π * r * (r + h)
Substituting the values:
1760 = 2π * r * (r + 6)
880 = π * r * (r + 6)
r^2 + 6r - 880/π = 0
Solving the quadratic equation, we get:
r ≈ 15.4 cm
6. Finding the volume of the cone:
Substituting the value of r in the volume formula, we get:
Volume = 2π * (15.4)^2 cm^3
≈ 1232 cm^3
Therefore, the volume of the cone is approximately 1232 cm^3. Hence, the correct answer is option D.
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Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer?
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Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer? for Banking Exams 2025 is part of Banking Exams preparation. The Question and answers have been prepared according to the Banking Exams exam syllabus. Information about Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Banking Exams 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer?.
Solutions for Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Banking Exams.
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Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Ratio of the breadth and length of the rectangle is 7:11 cm and the breadth of the rectangle is 8 cm more than the height of the cylinder. The total surface area of the cylinder is 1760 cm2 and the height of the cone is 2 cm more than the length of the rectangle. If the radius of the cone is half of the radius of cylinder and the perimeter of the rectangle is 72 cm, then what is the volume of the cone?a)616 cm3b)2464 cm3c)3672 cm3d)1232 cm3e)None of theseCorrect answer is option 'D'. Can you explain this answer? tests, examples and also practice Banking Exams tests.
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