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The height of a cylinder whose radius is 7 cm and the total surface area is 968 cm2 is:
- a)15 cm
- b)17 cm
- c)19 cm
- d)21 cm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The height of a cylinder whose radius is 7 cm and the total surface ar...
Total surface area = 2πr (h + r)
968 = 2 x 22/7 x 7 (7+h)
h = 15 cm
968 = 2 x 22/7 x 7 (7+h)
h = 15 cm
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Community Answer
The height of a cylinder whose radius is 7 cm and the total surface ar...
Understanding the Problem
To find the height of a cylinder, we need to use the formula for the total surface area (TSA) of a cylinder, which is given by:
TSA = 2πr(h + r)
Where:
- r = radius of the cylinder
- h = height of the cylinder
- π (Pi) is approximately 3.14
Given:
- Radius (r) = 7 cm
- Total Surface Area (TSA) = 968 cm²
Step-by-Step Calculation
1. Substituting Values:
- Replace r with 7 cm in the TSA formula:
TSA = 2 * π * 7 * (h + 7)
2. Calculating TSA:
- TSA = 2 * 3.14 * 7 * (h + 7)
- TSA = 43.96 * (h + 7)
3. Setting Up the Equation:
- Set the equation to the given TSA:
43.96 * (h + 7) = 968
4. Solving for h:
- Divide both sides by 43.96:
h + 7 = 968 / 43.96
h + 7 ≈ 22
5. Finding h:
- Subtract 7 from both sides:
h ≈ 22 - 7
h ≈ 15 cm
Conclusion
Thus, the height of the cylinder is 15 cm. Therefore, the correct answer is option 'A'.
To find the height of a cylinder, we need to use the formula for the total surface area (TSA) of a cylinder, which is given by:
TSA = 2πr(h + r)
Where:
- r = radius of the cylinder
- h = height of the cylinder
- π (Pi) is approximately 3.14
Given:
- Radius (r) = 7 cm
- Total Surface Area (TSA) = 968 cm²
Step-by-Step Calculation
1. Substituting Values:
- Replace r with 7 cm in the TSA formula:
TSA = 2 * π * 7 * (h + 7)
2. Calculating TSA:
- TSA = 2 * 3.14 * 7 * (h + 7)
- TSA = 43.96 * (h + 7)
3. Setting Up the Equation:
- Set the equation to the given TSA:
43.96 * (h + 7) = 968
4. Solving for h:
- Divide both sides by 43.96:
h + 7 = 968 / 43.96
h + 7 ≈ 22
5. Finding h:
- Subtract 7 from both sides:
h ≈ 22 - 7
h ≈ 15 cm
Conclusion
Thus, the height of the cylinder is 15 cm. Therefore, the correct answer is option 'A'.
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The height of a cylinder whose radius is 7 cm and the total surface area is 968 cm2 is:a)15 cmb)17 cmc)19 cmd)21 cmCorrect answer is option 'A'. Can you explain this answer?
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