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The curved surface area of a cylinder is equal to the total surface area of a cube whose each edge is 7 cm. If the height of the cylinder is 10 cm, what is its radius?
(π=22/7)
(π=22/7)
- a)3.5 cm
- b)5 cm
- c)7 cm
- d)10 cm
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The curved surface area of a cylinder is equal to the total surface ar...
Cube Total Surface Area = 6a2 = 6×72 = 6×49 = 294 cm2
Given
Curved Surface Area of cylinder = 294
Curved Surface Area of cylinder = 294
CSA = 2πrh
2 × 22/7 × r × 10 = 294
2 × 22/7 × r × 10 = 294
44r/7 ×10 = 294
(440r)/7 = 294
440r = 2058
r = 4.68 ≈ 5 cm
(440r)/7 = 294
440r = 2058
r = 4.68 ≈ 5 cm
So, option (b) is the correct answer.
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Community Answer
The curved surface area of a cylinder is equal to the total surface ar...
Understanding the Problem
To find the radius of the cylinder, we need to relate the curved surface area of the cylinder to the total surface area of a cube. Here are the steps:
Step 1: Calculate the Total Surface Area of the Cube
- The formula for the total surface area (TSA) of a cube is given by:
TSA = 6 * (edge length)^2
- Given that each edge of the cube is 7 cm:
TSA = 6 * (7^2) = 6 * 49 = 294 cm²
Step 2: Curved Surface Area of the Cylinder
- The formula for the curved surface area (CSA) of a cylinder is:
CSA = 2 * π * r * h
- Here, h (height of the cylinder) is given as 10 cm and we need to find the radius (r).
Step 3: Set Up the Equation
- According to the problem, the curved surface area of the cylinder equals the total surface area of the cube:
2 * π * r * h = 294 cm²
- Substituting h and π:
2 * (22/7) * r * 10 = 294
Step 4: Simplify the Equation
- 2 * (22/7) * r * 10 = 294
- This simplifies to:
(440/7) * r = 294
Step 5: Solve for Radius (r)
- Multiply both sides by 7:
440r = 294 * 7
- Calculate:
440r = 2058
- Divide both sides by 440:
r = 2058 / 440
- This gives:
r = 4.68 cm (approximately)
However, the answer choices suggest a rounding or approximation to the nearest whole number gives us:
Final Answer: Radius of the Cylinder
- The closest option is b) 5 cm.
This confirms that the radius of the cylinder is approximately 5 cm, which aligns with the options provided.
To find the radius of the cylinder, we need to relate the curved surface area of the cylinder to the total surface area of a cube. Here are the steps:
Step 1: Calculate the Total Surface Area of the Cube
- The formula for the total surface area (TSA) of a cube is given by:
TSA = 6 * (edge length)^2
- Given that each edge of the cube is 7 cm:
TSA = 6 * (7^2) = 6 * 49 = 294 cm²
Step 2: Curved Surface Area of the Cylinder
- The formula for the curved surface area (CSA) of a cylinder is:
CSA = 2 * π * r * h
- Here, h (height of the cylinder) is given as 10 cm and we need to find the radius (r).
Step 3: Set Up the Equation
- According to the problem, the curved surface area of the cylinder equals the total surface area of the cube:
2 * π * r * h = 294 cm²
- Substituting h and π:
2 * (22/7) * r * 10 = 294
Step 4: Simplify the Equation
- 2 * (22/7) * r * 10 = 294
- This simplifies to:
(440/7) * r = 294
Step 5: Solve for Radius (r)
- Multiply both sides by 7:
440r = 294 * 7
- Calculate:
440r = 2058
- Divide both sides by 440:
r = 2058 / 440
- This gives:
r = 4.68 cm (approximately)
However, the answer choices suggest a rounding or approximation to the nearest whole number gives us:
Final Answer: Radius of the Cylinder
- The closest option is b) 5 cm.
This confirms that the radius of the cylinder is approximately 5 cm, which aligns with the options provided.
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The curved surface area of a cylinder is equal to the total surface area of a cube whose each edge is 7 cm. If the height of the cylinder is 10 cm, what is its radius?(π=22/7)a)3.5 cmb)5 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about The curved surface area of a cylinder is equal to the total surface area of a cube whose each edge is 7 cm. If the height of the cylinder is 10 cm, what is its radius?(π=22/7)a)3.5 cmb)5 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The curved surface area of a cylinder is equal to the total surface area of a cube whose each edge is 7 cm. If the height of the cylinder is 10 cm, what is its radius?(π=22/7)a)3.5 cmb)5 cmc)7 cmd)10 cmCorrect answer is option 'B'. Can you explain this answer?.
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