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The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, the volume of cylinder (in cm3) is:
- a)3680
- b)4620
- c)6420
- d)5640
- e)Not Attempted
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The sum of the radius of base and height of a solid right circular cyl...
r + h = 37 . . .(1)
Total surface area of cylinder = 2πr(r + h) = 1628 cm2 . . . (2) (given)
Total surface area of cylinder = 2πr(r + h) = 1628 cm2 . . . (2) (given)
Substituting equation (1) in (2), we get:
⇒ 2πr × 37 = 1628
⇒ 74 ×22 × r ÷ 7= 1628
⇒ 74 ×22 × r ÷ 7= 1628
⇒ 74 × 22 × r = 11396
⇒ r = 11396 / (74 × 22)
⇒ r = 7
Using equation (1), we get:
h = 37 - 7
⇒ h = 30 cm
⇒ h = 30 cm
Therefore, the volume of the cylinder = πr2h
⇒ Volume= π × 72 × 30
⇒ Volume= 22 × 7 × 30 = 4620 cm3
Hence, the volume of the cylinder is 4620 cm3.
Most Upvoted Answer
The sum of the radius of base and height of a solid right circular cyl...
r + h = 37 . . .(1)
Total surface area of cylinder = 2πr(r + h) = 1628 cm2 . . . (2) (given)
Total surface area of cylinder = 2πr(r + h) = 1628 cm2 . . . (2) (given)
Substituting equation (1) in (2), we get:
⇒ 2πr × 37 = 1628
⇒ 74 ×22 × r ÷ 7= 1628
⇒ 74 ×22 × r ÷ 7= 1628
⇒ 74 × 22 × r = 11396
⇒ r = 11396 / (74 × 22)
⇒ r = 7
Using equation (1), we get:
h = 37 - 7
⇒ h = 30 cm
⇒ h = 30 cm
Therefore, the volume of the cylinder = πr2h
⇒ Volume= π × 72 × 30
⇒ Volume= 22 × 7 × 30 = 4620 cm3
Hence, the volume of the cylinder is 4620 cm3.
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Community Answer
The sum of the radius of base and height of a solid right circular cyl...
Given Information
- The sum of the radius (r) and height (h) of a cylinder is 37 cm:
r + h = 37
- The total surface area (TSA) of the cylinder is 1628 cm²:
TSA = 2πr(h + r) = 1628
Formulas Required
- Total Surface Area (TSA) of a cylinder:
TSA = 2πr(h + r)
- Volume (V) of a cylinder:
V = πr²h
Steps to Solve
1. Express Height in Terms of Radius:
From r + h = 37, we can express h as:
h = 37 - r
2. Substitute into TSA Formula:
Substitute h in the TSA equation:
2πr(37) = 1628
Simplifying gives:
74πr = 1628
r ≈ 7 cm (after solving)
3. Find Height:
Substitute r back to find h:
h = 37 - 7 = 30 cm
4. Calculate Volume:
Use the volume formula:
V = πr²h
V = π(7)²(30)
V = 1470π ≈ 4620 cm³ (using π ≈ 3.14)
Final Result
The volume of the cylinder is approximately 4620 cm³, which corresponds to option 'B'.
- The sum of the radius (r) and height (h) of a cylinder is 37 cm:
r + h = 37
- The total surface area (TSA) of the cylinder is 1628 cm²:
TSA = 2πr(h + r) = 1628
Formulas Required
- Total Surface Area (TSA) of a cylinder:
TSA = 2πr(h + r)
- Volume (V) of a cylinder:
V = πr²h
Steps to Solve
1. Express Height in Terms of Radius:
From r + h = 37, we can express h as:
h = 37 - r
2. Substitute into TSA Formula:
Substitute h in the TSA equation:
2πr(37) = 1628
Simplifying gives:
74πr = 1628
r ≈ 7 cm (after solving)
3. Find Height:
Substitute r back to find h:
h = 37 - 7 = 30 cm
4. Calculate Volume:
Use the volume formula:
V = πr²h
V = π(7)²(30)
V = 1470π ≈ 4620 cm³ (using π ≈ 3.14)
Final Result
The volume of the cylinder is approximately 4620 cm³, which corresponds to option 'B'.
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The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, the volume of cylinder (in cm3) is:a)3680b)4620c)6420d)5640e)Not AttemptedCorrect answer is option 'B'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, the volume of cylinder (in cm3) is:a)3680b)4620c)6420d)5640e)Not AttemptedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, the volume of cylinder (in cm3) is:a)3680b)4620c)6420d)5640e)Not AttemptedCorrect answer is option 'B'. Can you explain this answer?.
The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, the volume of cylinder (in cm3) is:a)3680b)4620c)6420d)5640e)Not AttemptedCorrect answer is option 'B'. Can you explain this answer? for UCAT 2025 is part of UCAT preparation. The Question and answers have been prepared according to the UCAT exam syllabus. Information about The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, the volume of cylinder (in cm3) is:a)3680b)4620c)6420d)5640e)Not AttemptedCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for UCAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 cm2, the volume of cylinder (in cm3) is:a)3680b)4620c)6420d)5640e)Not AttemptedCorrect answer is option 'B'. Can you explain this answer?.
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